Across:
1 Did a great job financially for The Company Men perhaps (TURNED A PROFIT) and recruited enemy agent (TURNED spy) at American (A) benefit (PROFIT) (TURNED A PROFIT),
10 Removes a public representative (UNSEATS) from new (-N-) chair (-SEAT-) in America (US = U-S) (UNSEATS),
11 Serving (PLATE-) a (-A-) university (-U) (PLATEAU) that’s plainly on the rise (PLATEAU),
12 Indian bread (NAAN) from Native American borders (‘NAtive AmericAN’ borders = NAAN),
13 The ball game played in Italy (BOCCE) is British (B-) football (soccer) with no wingers (no sides = ‘s’ + ‘r’) (‘soccer’ without ‘s’ + ‘r’ = -OCCE) (BOCCE),
15 Go around (TURN) with most of 30 across (most of ‘turns’ = TURN),
17 Thirsty without this (‘thirsty’ without ‘this’ = rty = TRY) to test (TRY),
19 Pressure (P-) to speak up (-UTTER) (PUTTER) in swinger’s club (swingers/golfers = PUTTER),
21 Address (SPEECH) for spinning (= reversal indicator) records (EPs = SPE-) and taking three types of drugs (ecstasy + cocaine + heroin = E+C+H = -ECH) (SPEECH),
22 Minor nobleman (BARONET) from a Bronte (a Bronte) novel (= anagram indicator) (a Bronte = BARONET),
23 Caught (-C-) copper (-CU-) cutting joint (joint = hip = HI-P) (HICCUP) – it’s a minor setback (HICCUP),
25 It (it) backfired (= reversal indicator) (it = TI-) on the British leaders (‘The British’ leaders = -TB-) and it (-IT) (TITBIT) is reported in the gossip column (TITBIT),
27 Millers leaving Marseilles (‘Millers’ leave ‘Marseilles’ = ase = SEA) in the Mediterranean (the Mediterranean SEA),
29 Sides of herring instead (sides of ‘HErring insteAD’ = HEAD) of complete salad? (HEAD of salad).
30 Chances to play (TURNS) more than one of the sides today? (‘turn’ on all sides of today’s grid + more than one ‘turn’ = TURNS),
31 Spot (spot = DAUB) a man from Clondalkin, for instance (Dub = D-UB), getting to grips with article (-A-) (DAUB),
34 The mean (AVERAGE) vegetarian drops tin (‘vegetarian’ drops ‘tin’ = vegeara = AVERAGE),
35 Disturb (UNHINGE) a foreign (a = UN-) element hanging around The Gate (-HINGE) (UNHINGE),
36 Passover? (TURN A BLIND EYE) It’s like Admiral Nelson to overlook it deliberately! (TURN A BLIND EYE attributed to Admiral Nelson).
Down:
2 The new arrogant type (UPSTART) of prince (-P-) in Stuart (Stuart = U-START) Reformation (= anagram indicator) (UPSTART),
3 Straight (NEAT) out of what’s revolutionary (= reversal indicator) in data encryption (what’s revolutionary in ‘daTA ENcryption’ = taen = NEAT),
4 Upsets (= reversal indicator) shirty types (tops = -SPOT) working on paper (ed = DE-) (DESPOT) for tyrant (DESPOT),
5 Secretary (PA-) has a lively tempo (-PACY) (PAPACY) in clerical office (PAPACY),
6 Dirge from Gore Vidal (‘dirge’ from ‘Gore Vidal’ = oval = OVAL) in a roundish way relates to Humpty Dumpty (OVAL),
7 Cools the bottle (ICE CUBE) for one (I-) Oriental (east = -E-) baby tiger (cub = -CUB-) found in Clare (-C-E) (ICE CUBE),
8 Presumably, one’s reaction to “Coming in From the Cold” (TURN UP THE HEAT) is to apply additional pressure (TURN UP THE HEAT),
9 Reverse positions positively (TURN THE TABLES) with the head (‘The’ head = T-) -hunter (hunter) working (= anagram indicator) (hunter = URN THE) for those employed in restaurant trade (TABLES) (TURN THE TABLES),
14 One of those airing the sentimental notes (CROONER) of mad (= anagram indicator) coroner (coroner = CROONER),
16 Entrance (DEBUT) is outstanding (debt = DEB-T) outside university (-U-) (DEBUT),
18 Awkward (= anagram indicator) topic (topic = OPTIC) for one on the bottle in the bar (OPTIC),
20 Strike (RAP) covered by The Telegraph (covered by ‘the telegRAPh’ = RAP),
21 Place (SET) for some horse trading (some ‘horSE Trading’ = SET),
24 Could start (‘Could’ start = C-) to loathe (-HATE-) a (-A -) classy (upper class = -U) (CHATEAU) nice source of wine (Nice/French source of wine from CHATEAU),
26 Turn a blind eye dismissing United? (‘turn a blind eye’ dismissing ‘united’ = rablnye = BLARNEY) You’ll hear this harmless nonsense in these parts! (‘gift of the gab’/‘blarney’ at the BLARNEY Stone),
27 Neighbour of Romanian (Serb = S-ERB) admits taking top off (c) trophy (‘cup’ without ‘c’ = -UP-) (SUPERB) and smashing? (SUPERB),
28 Technically, it’s a structure synonymous with Ring (ANNULI) to quash (ANNUL-) initial investment (initial ‘Investment’ = -I) (ANNULI),
32 Uplifting (= reversal indicator) characters from Unforgiven, Rawhide (characters from ‘unforgiveN RAWhide’ = nraw = WARN) and Sound the Alarm (WARN),
33 A Bandon (abandon = SHED) bank’s share price crumbled (banks ‘SHare price crumblED’ = SHED).