Thank you to Flimsy. Definitions are underlined in the clues.
Across
1. Leaders from Republic of Venezuela, in shock, producing agreement (8)
APPROVAL : 1st letters, respectively, of(Leaders from) “Republic of Venezuela” contained in(in) APPAL(to shock/horrify).
5. Models modelled on rare occasions (6)
SELDOM : Anagram of(… modelled) MODELS.
9. Original tour via Crete (8)
CREATIVE : Anagram of(tour) VIA CRETE.
Defn: …/inventive.
10. Something that’s done fighting lawsuit (6)
ACTION : Triple defn: 1st: …/an activity; 2nd: …/armed conflict; and 3: …/legal proceedings.
12. Head back inside casino in Oxford (5)
ONION : Hidden in(inside) reversal of(back …) “casino in Oxford“.
Defn: Slang for ….
13. Ought to reflect about small bears (9)
SHOULDERS : SHOULD(ought to/to necessarily perform) + reversal of(reflect) RE(with reference to/about) + S(abbrev. for “small”).
14. Was useful keeping record in mind (6)
HELPED : LP(abbrev. for a “long-playing record”/a phonograph recording format aka vinyl) contained in(in) HEED(to mind/to pay attention to).
16. Smart, I cleverly penned piece in the FT? (7)
ARTICLE : Hidden in(… penned) “Smart, I cleverly“.
19. Unnerved conductor with note (7)
RATTLED : RATTLE(Simon, British conductor) plus(with) D(a musical note, Re in the sol-fa system).
21. Air catching a queen’s loose skirt (6)
SARONG : SONG(an air/a melody) containing(catching) [A + R(abbrev. for “Regina”, a queen) ].
His and hers:
23. The evicted criminal avoiding H Poirot? (9)
DETECTIVE : Anagram of(… criminal) “The evicted” minus(avoiding) “H“.
Defn: An example of which/? is the fictional Hercule Poirot.
25. Break feet, by the sound of it (5)
PAUSE : Homophone of(…, by the sound of it) “paws”(an animal’s feet).
Defn: …/a temporary stop in action or speech.
26. Seafood stocks island holds (6)
CLAIMS : CLAMS(seafood/edible marine molluscs) containing(stocks) I(abbrev. for “island”).
Defn: …/maintains that something is true.
27. Disturbing prison gang (8)
STIRRING : STIR(slang for “prison”) + RING(a gang/a group of people in a shared activity).
28. Author sober before third of beers (6)
STERNE : STERN(sober/serious) plus(before) 3rd letter of(third of) “beers“.
Answer: Laurence …, Irish author.
29. Almost feel bitter about church after priest’s demeanour (8)
PRESENCE : [ “resent” (feel bitter about/bear a grudge against) minus its last letter(Almost) + CE(abbrev. for the Church of England) ] placed after(after) P(abbrev. for “priest”).
Defn: …/manner or appearance of a person.
Down
1. A new dock job — something on a ship? (6)
ANCHOR : A + N(abbrev. for “new”) + “chore”(a job/a task) minus its last letter(dock …).
2. Biden perhaps wrongly pretends to retain information primarily (9)
PRESIDENT : Anagram of(wrongly) PRETENDS containing(to retain) 1st letter of(… primarily) “information“.
Defn: Of which Biden of the USA is an example/perhaps.
3. Some Monet forgeries turned up frequently (5)
OFTEN : Hidden in(Some) reversal of(… turned up, in a down clue) “Monet forgeries“.
4. Suggested I saved obscure old penny (7)
ADVISED : Anagram of(… obscure) I SAVED + D(symbol for the penny, one of the former/pre-decimal British currency units).
6. Non-stop flight? (9)
ESCALATOR : Cryptic defn: Refering to the set/flight of stairs that moves continuously/non-stop, powered by electricity.
Ala spiral staircase:
7. Power from hot air reduced (5)
DRIVE : “drivel”(hot air/empty nonsensical talk) minus its last letter(reduced).
8. What you might call man embracing present member of the clergy (8)
MINISTER : MISTER(what you might call/a form of address for a man) containing(embracing) IN(present at one’s home, office or a gathering, as in “only his secretary was present when I arrived”.
11. Party’s picked up with a drink (4)
SODA : Reversal of(… picked up, in a down clue) [DO(a party/a social function)‘S ] plus(with) A.
Defn: A carbonated ….
15. New epic lemon peelers (9)
POLICEMEN : Anagram of(New) EPIC LEMON.
Defn: …, a term derived from Sir Robert Peel, founder of the Metropolitan Police.
17. Prisoner marrying, creating bewilderment (9)
CONFUSION : CON(short for “convict”/prisoner) + FUSION(marrying/a joining together).
18. Consequences for channels (8)
PRODUCTS : PRO(for/in favour of) + DUCTS(channels/tubes for conveying gases and liquids).
Defn: …/that which result from an action.
20. Weak person, I’d shed first tear (4)
DRIP : “I’d” minus its 1st letter(shed first) + RIP(to tear/split forcefully).
21. Perspiring more, I removed jumper (7)
SWEATER : “sweatier”(perspiring/giving out sweat more) minus(… removed) “I“.
His and hers:
22. Something that could make you shiver after initially leaving European Union (6)
LEAGUE : AGUE(something that could make you shiver, in this case a fever that causes recurring sweating and shivering) placed below(after, in a down clue) 1st letters, respectively, of(initially) “leaving European“.
Defn: …/a group of people, countries or groups coming together for mutual cooperation.
24. Make fun of the batsmen regularly missing (5)
TEASE : “the batsmen” minus its 2nd and every other letter thereafter(regularly missing).
25. Drinks vessels might be found here (5)
PORTS : Double defn: 1st: A fortified wine originally from Portugal; and 2nd: 
Thanks Flimsy for an enjoyable puzzle and scchua for the colourful, detailed and neat blog!
My top picks today are PRESENCE, ANCHOR, MINISTER and DRIP.
Thanks Flimsy and scchua. I found 17dn confusing at first, but of course “marrying” as a verbal noun defines FUSION perfectly well. The school of thought that allows ambiguities to be resolved by checked letters seems to be fully in the ascendant.
PB @2: I found 17dn confusing at first – that’s brilliant. Yes, there is the potential for two answers there and the use of the gerund could mislead. That aside, I found this a very enjoyable puzzle with lots of clean and often concise cluing. Plenty of likes including SELDOM, DETECTIVE, CLAIMS, ESCALATOR, MINISTER and SWEATER.
Thanks Flimsy and scchua
Another one who had ‘confusing’ for 17dn as I thought the definition was ‘Creating bewilderment’. This led to me struggling to fit a word like ‘presages’ into 29ac which obviously did not work. As PB said once I had the crossing letters and checked my answers all was resolved. I found this a quick save for the south east corner. Thanks setter and blogger.
A straight-forward and breezy solve with crystal clear parsing. [I already had PRESENCE so no confusing CONFUSION].
Top picks were STIRRING, SARONG (nice pics, Scchua!) and DETECTIVE.
Thanks to Flimsy and Scchua.
Liked ESCALATOR. [Spiral ESCALATORs – what will they think of next?]
Thanks F&s
What Diane@5 wrote. I also liked ESCALATOR
I think this may be my first time doing a Flimsy puzzle and I enjoyed it
Thanks Flimsy and scchua
What Martyn and FrankieG wrote. It was a first Flimsy for me too. Enjoyed the pictures which usually lift the spirits.
Thanks Flimsy and Scchua.
Adrian@4. It’s Val and Jayne.