Good puzzle to kick off the week.
A few clues were tricky – not heard of 1a for example, but deduced it from the crossers. 26a feels a bit too literal? 4d should raise a few eyebrows… Otherwise a good challenge. Favourites include RHINE, MAINBRACE, DRESSINGS, and CAYENNE. Thank you Crux!

Across
1 Bird, dog or butterfly (11)
SWALLOWTAIL
SWALLOW (bird) + TAIL (dog)
7 What’s wrong with skiing regularly? (3)
SIN
S[k]I[i]N[g] (regularly)
9 A way in sought by jewel thief? (5)
AGATE
Double definition
10 Most important couple spliced at sea (9)
MAINBRACE
MAIN (most important) + BRACE (couple)
From the saying “splice the mainbrace”
11 Doctor points signs out in Russian and French for example. (9)
DRESSINGS
DR (doctor) + E,S (points) + (SIGNS)* (*out)
12 Large river beast needs energy for love (5)
RHINE
RHIN[o] (Beast, needs E (energy) for O (love))
13 21, lazy, heartless and materialistic (7)
EARTHLY
EARTH (21d, sphere) + L[az]Y (heartless)
15 Fish fingers start to go missing (4)
EELS
[f]EELS (fingers, start to go missing)
18 Some fall back into an ambush (4)
TRAP
(PART)< (some, <fall back)
20 Kitty Nolan’s 16, said to be really hot (7)
CAYENNE
“K.N.” (Kitty Nolan’s 16d (initials) “said”)
23 Put in water pipes exactly (5)
PLUMB
Double definition
24 It’s rare, it mutates, then itches (9)
IRRITATES
(ITS RARE IT)* (*mutates)
26 Rule from Strasbourg? (9)
EUROCRACY
Cryptic definition
27 A council district grant (5)
AWARD
A WARD (a council district)
28 You have to finish in seven days, or ten, definitely (3)
END
in [sev]EN D[days] or [t]EN D[efinitely]
29 Highly placed asset of the CIA? (3,2,3,3)
SPY IN THE SKY
Cryptic definition
Down
1 She’s entertaining and gets one mixed drinks (8)
SHANDIES
SHE’S entertaining AND gets I (one)
2 Rewrites are a must for these dabblers (8)
AMATEURS
(ARE A MUST)* (*rewrites)
3 Yorkshire city heads speak out (5)
LEEDS
“Leads” (heads, “speak out”)
4 Female warrant officer, strong and steadfast (7)
WOMANLY
WO (warrant officer) + MANLY (strong and steadfast)
5 A paper is in dispute (2,5)
AT ISSUE
A TISSUE (a paper)
6 A party going on half July in a big way (9)
LIBERALLY
LIBERAL (a party) going on [ju]LY (half)
7 Assist in motion, or its opposite (6)
STASIS
(ASSIST)* (*in motion)
8 Massaged for an audience as required (6)
NEEDED
“kneaded” (“massaged”, for an audience)
14 Tough players on the team’s books (9)
HARDBACKS
Double definition
16 Familiar paper often referred to by them (8)
INITIALS
Cryptic definition: referring to FT
17 Hardly a Lenten celebration (5,3)
FEAST DAY
Cryptic definition
19 School colours like red and blue (7)
PRIMARY
Double definition
20 Such British comedies make a fuss (5-2)
CARRY ON
Double definition
21 Field the ball (6)
SPHERE
Double definition
22 Rotten place – yet free! (6)
PUTRID
PUT (place) + RID (free)
25 Dreadful cheat, this pirate (5)
TEACH
(CHEAT)* (*dreadful)
Thanks, Teacow — yes, it was a mixed bunch. I’d put 20dn with 26ac; and yet your favourites (also mine) were effulgent. But fun as always — thanks, Crux.
Interesting that 4D is considered to be open to sexist interpretation, but the Lolita-like surface reading of 20A does not merit comment for its sheer creepiness.
Slow going for me; took several sittings to complete. I did know SWALLOWTAIL because it and the monarch are the two butterflies I see regularly. Never heard of MAINBRACE. I don’t get how TEACH means pirate but nothing else made sense as an anagram of cheat. Thought CAYENNE was brilliant. Thanks Crux and Teacow for parsing.
Edward Teach was the real name of the pirate Blackbeard. I know, it’s pretty arcane.
Thanks to Crux and Teacow. Enjoyable. I did know TEACH the pirate but I started with Eye, not SPY IN THE SKY so I took a while getting HARDBACKS.
Thanks Crux and Teacow
Reasonably straightforward although I didn’t make life easy by bunging in an unparsed STAND-UP at 20d originally. Didn’t know of the phrase ‘splice the main brace’ which makes the clue much better.
Actually had HARDBACKS as a charade of HARD (tough) + BACKS (players on the team). Finished with the linked CAYENNE and INITIALS clues which I liked a lot.