Across:
1 They set off the explosive types (TIMERS) opening 14 across (‘time exposure’ = TIME-) and starting religious (starting ‘religious’ = -R-) school (-S) (TIMERS),
4 Play emotional games with (PSYCH OUT) foreign (= anagram indicator) spy (spy = PSY-) caught (-C-) with Bellow (bellow = shout) losing the head (s) (‘shout’ without ‘s’ = -H OUT) (PSYCH OUT),
9 Haunted out of Chateaubriand (‘haunted’ out of ‘Chateaubriand’ = cabria = ARABIC), or that’s what they’re saying in Tunis (ARABIC),
10 Behind the scenes (OFF STAGE) it’s not fresh enough (OFF) for Gate’s (gates = STAGE) production (= anagram indicator) (OFF STAGE),
12 Auntie got (auntie got = EATING OUT) drunk (= anagram indicator) taking advantage of what’s in The Bistro (EATING OUT),
13 Soldier on without Nero (‘soldier on’ without ‘Nero’ = soldi = IDOLS) and the rest of the false gods (IDOLS),
14 Prison term (TIME) for public nudity perhaps (EXPOSURE) (TIME EXPOSURE) manipulated by the photographer (TIME EXPOSURE),
18 Papers’ (papers = IDENTITY CARD) name (IDENTITY) for The Queen? (CARD) (IDENTITY CARD),
21 Sample of vindaloo fare (sample of ‘vindaloo fare’ = ALOOF) can be reserved (ALOOF),
22 Alternatively (OR-), revolutionary’s (Che’s = -CHES-) art (art = -TRA) review (= reversal indicator) (ORCHESTRA) is producing the numbers (ORCHESTRA),
24 Notices a (notices a = CANOEIST) lark (= anagram indicator) paddling in the water (CANOEIST),
25 Sour (sour = -OURS-) exchange (= anagram indicator) between Belgium (B-E) (BOURSE) and France’s stock market (BOURSE),
26 Potential private dinner date (army MESSMATE) in trouble (MESS-) with partner (-MATE) (MESSMATE),
27 Transfer (= anagram indicator) debits (debits = BEDSIT) for temporary accommodation (BEDSIT).
Down:
1 To see the world (travel) mostly (l) (‘travel’ without ‘l’ = TRAVE-) with a sore eye (-STY) (TRAVESTY) is a poor substitute for the real thing (TRAVESTY),
2 Opportunity to enjoy 12 across, for example (opportunity to enjoy ‘eating out’ = MEALTIME), or Breakfast at Tiffany’s, for instance (MEALTIME),
3 Briefings don’t include FBI’s (‘briefings’ don’t include ‘FBIs’ = reing = REIGN) time in absolute control (REIGN),
5 Security (SAFETY) at Exchange (SWITCH) (SAFETY SWITCH) saves you getting a shock (SAFETY SWITCH),
6 Funny (= anagram indicator) comics (comics = COSMIC) in school (RAY) (COSMIC RAY) produced by traveller at the speed of light (COSMIC RAY),
7 A rotor (a rotor = ORATOR) replaced (= anagram indicator) in one of the speakers (ORATOR),
8 Devout type (THEIST) of teller from the start (‘teller’ from the start = T-) gets bank job (-HEIST) (THEIST),
11 Escort (COMPANION) gets to place (SET) (COMPANION SET) in The Stand where poker is appreciated (COMPANION SET),
15 It’s a classy time to leave (END OF TERM) when the delivery is expected (END OF TERM),
16 Designs for the materials (PATTERNS) for new (= anagram indicator) transept (transept = PATTERNS),
17 Next (ADJACENT) to Bill (AD-) on one side, Jack (on one side ‘Jack’ = -JA-) is one of those types that is spent (-CENT) (ADJACENT),
19 Gangster (-AL- Capone) followed by copper (-CU-) consumed by thulium (T-M) (TALCUM) – a white powdery substance (TALCUM powder),
20 Horses for courses (MOUNTS) in Leinster, for example (MOUNT- Leinster), and Saracens for the final (‘Saracens’ for the final = -S) (MOUNTS),
23 Call up (EVOKE) First Lady (EV-E) over fine (fine = okay = -OK-) (EVOKE).