Across:
1 What it's got is not everyone's cup of tea (LIMITED APPEAL), as only one player made a plea to the umpire (LIMITED APPEAL),
10 A deceit (a deceit) performed (= anagram indicator) (a deceit = ICED TEA)) by one of those typically drunk in the summer (ICED TEA),
11 Whips up (= reversal indicator) a bit of mayo (Co Mayo/Cong = GNOC-) to go with head of cavolo (head of “Cavolo” = -C-) – it’s a salute (-HI) (GNOCCHI) to Italian cuisine (GNOCCHI),
12 Held by Guggenheim – a museum (held by ‘guggenheIM A Museum’ = IMAM) preaching to the faithful (IMAM),
13 Clone from well-chosen (‘clone’ from ‘well chosen’ = welhs = WELSH) type from a neighbouring island (WELSH),
15 Uplifting (= reversal indicator) fragment of favourite yarn (some ‘favourITE Yarn’ = itey = YETI) of The Abominable Snowman (YETI),
17 It’s on fire (LIT) over (= reverse indicator) in Antilles (over in ‘anTILles’ = til = LIT),
19 Sweetheart (‘swEet’ heart = E-) gets to glance through (-SKIM-) final scenario (final ‘scenariO’ = -O) (ESKIMO) produced by a cold type up north (ESKIMO),
21 Juliet (J-) stole (stole) whip (= anagram indicator) (stole = -OSTLE) (JOSTLE) from jockey (jockey/scramble = JOSTLE),
22 Under par (ILL-) and leading Invitational (leading ‘Invitational’ = -I-) briefly (e) – single out for praise (cite) (‘cite’ without ‘e’ = -CIT) (ILLICIT) or is that forbidden? (ILLICIT),
23 Tap dancers ignoring pest (‘tap dancers’ ignoring ‘pest’ = adancr = CANARD) is a baseless rumour (CANARD),
25 Those areas around Hull (ship’s hull / BILGES) and backward (= reverse indicator) parts of Leeds, e.g., liberated (backward parts of ‘leedS EG LIBerated’ = seglib = BILGES),
27 You bet (you bet! = YES) it’s found over (= reverse indicator) in exercise yard (in ‘exerciSE Yard’ = sey = YES),
29 Responsibility (ONUS) of old (O-) star (sun) retiring (= reverse indicator) (sun = -NUS) (ONUS),
30 A number of characters committed a crime (a number of characters ‘commitTED A Crime’ = tedac) setting up (= reversal indicator) (tedac = CADET) trainee officer (CADET),
31 Knocking back (= reverse indicator) containers (pots = STOP) of Scotch? (scotch/put an end to = STOP),
34 Wind (CHINOOK) in church (CH-) from one (-I-) alcove (-NOOK) (CHINOOK),
35 Young man (lad) carrying back (= reverse indicator) (lad = D-AL) one (-I-) vase (-URN-) (DIURNAL) during the day (DIURNAL),
36 In the short term (LIMITED PERIOD) it’s inadequate (LIMITED) – full stop (PERIOD) (LIMITED PERIOD).
Down:
2 Swell treatment (ICE PACK) of one (I-) church (Church of England = -CE) group (PACK) (ICE PACK),
3 Tiny amount (IOTA) of cases dropped by associate (‘cases’ dropped by ‘associate’ = oiat = IOTA),
4 Celebrity (-NAME-) in the foreign (‘the’ Spanish = E-L) (ENAMEL) glossy coat synonymous with The Crown? (ENAMEL),
5 31 days (AUGUST) with precious type (gold = AU-) from Air Force? (air force = -GUST) (AUGUST),
6 Tips for people running (tips for ‘People Running’ = PR-) around (-O-) department (-D) (PROD) getting jab (PROD),
7 As old as The Hills (ANCIENT) in 20 down similarly (‘old’ similar to ANCIENT),
8 Told stories (lied = LI-ED) about American university (Massachusetts Institute of Technology = -MIT-) having pick (CHOICE) (LIMITED CHOICE) of finite selection (LIMITED CHOICE),
9 Endless (s) caps (limits) (‘limits’ without ‘s’= LIMIT-), tops, evening dresses (tops/first letters of ‘Evening Dresses’ = -ED) and stock (SUPPLY) (LIMITED SUPPLY) that’s only available in small quantities (LIMITED SUPPLY),
14 In short supply (LIMITED) on all sides today (LIMITED on all sides of today’s grid),
16 Unpleasant smile (SMIRK) from Old Bob (‘old bob’ = shilling = S-) Bond’s boss (-M-) getting to make cross (make cross/annoy = -IRK) (SMIRK),
18 Misfortune to lose nurse (‘misfortune’ to lose ‘nurse’ = mifot = MOTIF) by design? (MOTIF),
20 Bill’s partner in the British police force (OLD Bill) is not young (OLD),
21 Ship’s sail (JIB) opens just in battle (opens/first letters of ‘Just In Battle’ = JIB),
24 Jubilation failing to get job (‘jubilation’ putting out ‘job’ = uilatin = NAUTILI) with the swimmers? (NAUTILI),
26 Take up a habit (GET INTO) and begin to enjoy it (GET INTO),
27 Jerk (YANK-) on drugs (Es / E+E = -EE) (YANKEE) from The New Yorker (YANKEE),
28 Make fun of (SEND-UP) insured person losing Renoirs (‘insured person’ losing ‘Renoirs’ = sudpen = SEND-UP),
32 Points of interest perhaps (FOCI) covered up (= reverse indicator) by public office (covered by ‘publIC OFfice’ = icof = FOCI),
33 The whirling, ringing sound (BURR) of Rock? (siliceous rock = BURR).