Thank you to Basilisk. Definitions are underlined in the clues.
Across
1. Chief police officer connected with sex cases (8)
CARDINAL : DI(abbrev. for “detective-inspector”, a police officer) contained in(… cases) CARNAL(connected/pertaining to sexual needs and activities, or anything physical).
5. Less sensitive issue (6)
NUMBER : Double defn: 2nd: … of a periodical publication.
10. Apricot tart contains dairy (7)
RICOTTA : Hidden in(… contains) “Apricot tart“.
Defn: An example of “dairy”/collectively, milk and milk products).
11. Primate with time for priest’s wild vision (7)
CHIMERA : “chimp”(short for “chimpanzee”, the primate that is human’s closest living relative) with ERA(a long time period) replacing(… for …) “p”(abbrev. for “priest”).
Defn: …/a fancy.
12. Can region spread enlightenment? Absolutely not! (9)
IGNORANCE : Anagram of(… spread) CAN REGION.
13. Minute appearance of actor on stage (5)
ENTRY : Double defn: 1st: One of the items recorded/entered into the minutes of a proceeding/meeting, say.
Is the 1st definition a bit stretched?
15. Harsh electronic form of music (5)
GRIME : GRIM(harsh/severe) + E-(prefix indicating an electronic item).
Defn: …, specifically a style of British rap.
16. Layabout hit sentry out of uniform (8)
SLUGGARD : SLUG(to hit/to strike a hard blow) + “guard”(a sentry) minus(out of) “u”(abbrev. for “uniform”).
19. Family group has assistance withdrawn before vitriolic attack (8)
DIATRIBE : TRIBE(an extended family group) placed after(has … before) reversal of(… withdrawn) AID(assistance/help).
20. Sit on horse led by British groom’s mate (5)
BRIDE : RIDE(to sit and travel on a horse) placed after(led by) B(abbrev. for “British”).
21. Ancient philosopher connecting prophecy with Nicodemus (5)
CYNIC : Hidden in(connecting … with …) “prophecy” “Nicodemus“.
Defn: One practising the ancient Greek philosophy of Cynicism.
23. JFK or Nixon could be seen as a product of the Masons? (9)
STONEWORK : STONE(Oliver, controversial American film director) + WORK(a product/one’s output, an example of which, in Stone’s case are the films, JFK or Nixon).
Defn: …, or “masons”/craftsmen working with stone.
25. Little-known remedy for patient being deprived of lead? (7)
OBSCURE : CURE(remedy/a measure taken to eliminate a condition) placed after “Job”(the patient being/person in the Bible) minus its 1st letter(deprived of lead)’S(indicating possession/for)
27. Number one trend turned into issue (7)
EDITION : Reversal of(… turned) [ NO(abbrev. for “number”) + I(Roman numeral for “one”) + TIDE(trend of events/the way things are going) ].
Defn: cf. 5 across.
28. Think about inspiring good man (6)
KNIGHT : Anagram of(… about) THINK containing(inspiring) G(abbrev. for “good”).
Defn: … on the chessboard.
29. Single male part transposed by composer (8)
BACHELOR : Reversal of(… transposed) ROLE(a part in a play, say) placed after(by) BACH(the most prominent member of the musical family was Johann Sebastian, German composer of the Baroque period).
Down
1. Conservative replaces leader of union in Hackney? (8)
CARRIAGE : C(abbrev. for a member of the Conservative Party) replacing(replaces) 1st letter of(leader of) “marriage”(a matrimonial union).
Defn: … is an example of this type of vehicle.
2. Restore electron emitted by mysterious charged particle (11)
RECONDITION : “e”(symbol for “electron” in physics) deleted from(emitted by) “recondite”(mysterious/little known) + ION(a charged particle/an atom or group of atoms carrying an electric charge).
3. Cross about Bury firm’s clothing (9)
INTERSECT : C(abbrev. for “circa”/about or approximately in reference to years or other periods of time) contained in(… clothing) [ INTER(to bury in a grave or tomb) + SET(firm/not likely to change) ].
4. Con cleaning out good person once more (5)
AGAIN : “against”(con/not supporting, in contrast to “pro”) minus(cleaning out) “st”(abbrev. for “saint”/a good person).
6. Make one and one equal to begin with (5)
UNITE : UNIT(one/an individual thing or person) + 1st letter of(… to begin with) “equal“.
7. Farewell aside to the audience (3)
BYE : Homophone of(… to the audience) “by”(aside/next to).
8. Prepare to discover the meaning of unknown quantity (5)
READY : READ(to discover the meaning of/to understand written or printed matter, or even a facial expression, say) + Y(symbol for an unknown quantity in maths).
9. Broadcaster’s dropped Christmas programme (8)
SCHEDULE : Homophone of(Broadcaster’s) [ “shed”(dropped/discarded) + “Yule”(an archaic term for “Christmas”) ].
Defn: … specifying when a series of activities should happen.
14. Rioter burst into hearing related to land (11)
TERRITORIAL : Anagram of(… burst) RIOTER contained in(into) TRIAL(a hearing in court).
16. Bridge partnership stops priest playing Old Maid (8)
SPINSTER : N,S(abbrev. for “North” and “South” respectively, denoting partners in the card game of bridge) contained in(stops) anagram of(… playing) PRIEST.
17. Send up husband and father beginning to believe extravagant nonsense (9)
GIBBERISH : Reversal of(Send up, in a down clue) [ H(abbrev. for “husband”) plus(and) SIRE(a father) + 1st letter of(beginning to) “believe” + BIG(extravagant/excessive) ].
18. Believe head of state’s a tool of the Treasury? (8)
RECKONER : RECKON(to believe/to have a particular opinion) + ER(abbrev. for “Elizabeth Regina”, the Queen, head of state of the UK).
Defn: A table or device to assist with calculations, financial ones in the Treasury.
A table: 
, and an ancient tool:
21. Notice club’s top rugby player (5)
CLOCK : 1st letter of( …’s top, in a down clue) “club” + LOCK(a rugby player in the second row of a scrum).
Defn: Slang for ….
22. Press put down object of affection (5)
CRUSH : Triple defn: 1st: …/to exert pressure on; 2nd: …/to violently subdue, say, an uprising; and 3rd: …/the person with whom one is infatuated/has a crush on.
24. Upset about parking in middle of road works (5)
OPERA : Reversal of(Upset, in a down clue) [ RE(about/with reference to) + P(abbrev. for “parking”) ] contained in(in) the 2 central letters of(middle of) “road“.
Defn: A collective term for dramatic works set to music for singers and instrumentalists.
26. Go downhill rapidly and almost miss out (3)
SKI : Last letter deleted from(almost) “skip”(to miss out/to omit)
Tough stuff, elegantly set. I particularly liked the boundary answers. Thanks to both: scchua had his work cut out this morning!
Today’s highly entertaining grid from Basilisk was further enhanced by the perimeter pairs which helped land, among others, 21d and my LOI 23a.
Favourites 1a/5 and 10, with nods to 12, 14, 17, 21d.
Thanks to Basilisk and Scchua
Needed the perimeter pairings to get RECKONER. Guessed STONEWORK from ‘product of the Masons’ but didn’t know the Oliver Stone films. Wasted a bit of time trying to get ‘coital’ round a 2 letter word for police officer in 1a and trying to find an anagram of trimate meaning ‘vision’ for 11a. As usual, I marvel at the skill of this setter. I’m sure I’ve seen many clues for OPERA before but 24d outclassed them all.
Thanks Basilisk and scchua
25ac: I think you have to take “remedy for patient” as a phrase meaning JOB’S CURE, which is then deprived of its first letter. The parsing currently given is missing the S.
21dn: Here I think the “top” indicates first letter of the word “club” rather than an abbreviation.
I wondered how many of the solvers outside the UK were familiar with the pronunciation of “schedule” with a silent C.
I saw CARDINAL NUMBER and KNIGHT BACHELOR but missed the READY RECKONER connection-CARRIAGE CLOCK didnt ring any bells snd I messed up 6d putting UNION instead of UNITE
But I did notice GRIMES in the grid which is an OPERA
Thanks all
Enjoyable as ever from Basilisk. I thought GIBBERISH was as good a reversal as I’ve seen for a long time and the pairs of words around the perimeter were a nice touch.
I’m outside the UK but am definitely a soft C SCHEDULE pronouncer and although it probably shouldn’t, the hard C pronunciation, which I think of as American, always grates with me.
Not being familiar with the musical genre, is 15a an all-in-one?
Thanks to scchua and Basilisk
WordPlodder @7. Thanks for that. The hard C pronunciation doesn’t grate with me and, let’s face it, we hear both pronunciations here in the UK and I wouldn’t be at all surprised if the hard C is more common. I’m 65 and have heard both all my life so not a new thing. What I don’t know is which countries adopt UK English and which American. For the record, I use “shed yule”.
I agree with Pelham Barton@4 that the S is needed in 25a, but I think, probably pedantically, that then one has to take it as “remedy for patient being” – Job is a patient being, rather than a patient. A good puzzle – though I totally failed to notice the perimeter connections.
Another enjoyable battle with Basilisk – I did notice the perimeter words too – my particular favourite was the deprived of lead patient being
Thansk to Basilisk and scchua
Perplexus, I think we’re on the same page re 25a, but I inadvertently omitted the “S”. Blog amended to make my parsing clearer.
Pelham Barton, thanks for the 21d correction.
Re the “schedule” pronunciation, I believe it depends on where you went to shool?
Perplexus @9 re 25ac: I agree with that. “Being” should indeed be part of the definition.
Thanks for a very clear blog on a tough puzzle, totally missed the pairings . Many sound, clever clues here , too many to list. Very minor quibble for 2D, there are two electrons in recondite.
Correction to 12: I should have said part of the definition of Job, not of the answer. So, for the avoidance of doubt, I think the overall parsing for 25ac goes
Little-known: definition of the answer OBSCURE
remedy for patient being: taken together as a phrase for JOB’S CURE
deprived of lead: indication to remove the J.
While enjoying clues like OBSCURE, SCHEDULE, CHIMERA, EDITION, and BACHELOR I found a good bit of this beyond my grasp. Thanks to both.
We found this quite a challenge and went off up several blind alleys (e.g. trying to make an anagram of ‘trimate’ in 11ac) before getting it all – and it wasn’t till we’d finished that we spotted the perimeter pairs. Favourite was GIBBERISH.
Thanks, Basilisk and scchua.
Many thanks to scchua for the blog and to everyone who has been kind enough to comment.
Thanks Basilisk and scchua
Late to this as I made a last effort on Gozo’s Christmas puzzle (and still three to go – 🙁 )
One always knows that one is in for a battle with this setter – and it always a pleasant and satisfying one when you get it done. Took more than twice my average time to fill the grid here – and three that required extra post thinking to get the parsing out – 23a, 2d and 24d. New term for the day was GRIME.
Lots of devices used throughout and some clever misdirection in many of them. Finished in the SE corner with BACHELOR, the very clever OPERA (such great use of surface reading to steer one away from what is really wanted) and RECKONER the last one in. After such a workout, was too puffed out to see the perimeter pairings !