Across:
1 Acted the eejit (PLAYED THE FOOL) and deceived (PLAYED) Nick Bottom, for instance (Nick Bottom is THE FOOL in Shakespeare’s A Midsummer Night’s Dream) (PLAYED THE FOOL),
10 The foreign (the = LA-) chronicle (saga = -SAG-A) about Nationalist (-N-) (LASAGNA) dishy type between the sheets (LASAGNA / also lasagne),
11 Sets off (= anagram indicator) alarm – it (alarm it = MARTIAL) relates to those who might be in the wars? (MARTIAL),
12 Reverses (= reversal indicator) wagon (dray = YARD) out the back (YARD),
13 Sycophants (yes men) dismiss head of state (head of “state” = s) (“yesmen” dismiss “s” = YEMEN) in Asian country (YEMEN),
15 Challenge (PLAY) for most of (s) 30 across (“plays” without “s” = PLAY),
17 Ruin (MAR) in Montmartre? (in “Montmartre” = MAR),
19 The devil’s (devils = DEMONS) tattle removed from Old Testament (“tattle” removed from “Old Testament” = odsmen = DEMONS),
21 It’s revolting (PUTSCH is an uprising/coup) place (PUT-) for small (-S-) church (-CH) (PUT SCH),
22 Good books (Old Testament = OT-) can be a conversation starter (-HELLO) (OTHELLO) or a tragedy (OTHELLO),
23 Reports (= homophone indicator) state (“Hungary” = “HUNGRY”) is fundamentally empty (HUNGRY),
25 More than one Doubting Thomas (CYNICS) upsets every (= reverse all indicator) barman (senior counsel = SC = -CS) from one (-I-) American city (New York City = CYN-) (CYNICS),
27 Naturally occurring material (ORE) found in rainforests (found in “rainforests” = ORE),
29 Record (LIST) by composer (“Liszt’ = “LIST”) on the radio (= homophone indicator),
30 Puts on boots (PLAYS) for more than one side today (PLAYS),
31 Gives a helping hand (AIDS) in some air-raid shelters (some “air raid shelters” = AIDS),
34 The lead (A) in Antigone (lead of “Antigone” = A) at The Abbey (priory) isn’t finished (y) (“priory” without “y” = PRIOR-) – for one (-I) (A PRIORI), that’s based on theoretical deduction (A PRIORI),
35 Rescue (SALVAGE) pupil (learner = -L-) in wild (SA-VAGE) (SALVAGE),
36 Back (PLAY THE PONIES) on the theatre (PLAY) with most of (m) them (“them” without “m” = THE) in the stalls (PONIES) (PLAY THE PONIES).
Down:
2 Really strong desire (LUST-) for drink (-RUM) (LUSTRUM) for a number of years (five years = LUSTRUM),
3 Healthy workout (YOGA) for characters in Mayo gang (characters in “Mayo gang” = YOGA),
4 Crown (DIADEM) and diamonds (D-) one (-I-) made (made = -ADEM) to order (= anagram indicator) (DIADEM),
5 Pound (HAMMER) – one of the symbols of old European country? (HAMMER & Sickle),
6 Both sides of funny story (both sides of “funny story” = FURY) in Spitfire (spitfire/rage = FURY),
7 Produced (= anagram indicator) rose oil (rose oil = ORIOLES) for the birds (ORIOLES),
8 Dramatic work (PLAY-) by writer (ED) of The Spanish (the = el = -E L-) in Death (death = TH- -EAD) rubbished (= anagram indicator) (PLAYED THE LEAD) – did The Star do it? (PLAYED THE LEAD),
9 Jam (PLAY) and Status Quo (THE SYSTEM) (PLAY THE SYSTEM) exploit a loophole to their advantage (PLAY THE SYSTEM),
14 Bananas (MAD-) from country (Eire) cut short (e) (“Eire” without “e” = -EIR-) for a (-A) (MADEIRA) cake (MADEIRA cake),
16 Sounds like something coming out of 24 down (SNORE coming out of “nostril”) will annoy one with retirement plan? (will annoy one with retirement plan/plan to go asleep = SNORE),
18 Transport (BU-S) carrying around (-O-) young leader (“young” leader = -Y-) (BUOYS) from the Sea Guides (BUOYS),
20 One of those maybe in half of 28 down (half of “eyes up” = eye / STY) can be messy (pig STY),
21 Type of company (PLC) to pullback sacrificing Kabul (“pullback” sacrificing “Kabul” = plc = PLC),
24 Relative (son = NOS-) returns (= reversal indicator) to Trim (Trim) briefly (m) (“Trim” without “m” = TRI-) from Lima (-L) (NOSTRIL) for a breather (NOSTRIL),
26 Copy (IMITATE) from Ireland (Ireland domain = i.e. = I-E) all over US College (Massachusetts Institute of Technology = -MIT-) and a (-A-) writer’s centre (“writers” centre/middle letter = -T-) (IMITATE),
27 Loses the head (c) with unfriendly type (“coldish” without “c” = OLDISH) that’s not getting any younger (OLDISH),
28 Suggestively looks at (EYES UP) record (extended-play record = E- -P) about what’s agreed (agreed! = -YES-) at university (-U-) (EYES UP),
32 Shape (BODY) of one of the builders (BODY builder),
33 Some roadmap languishing (some “roadmap languishing” = PLAN) in architect’s drawer (PLAN).