ACROSS
5. C_K_ D_A_ inside JAW = JACKDAW <flyer>
9. ORATE outside (IG + IN) = ORIGINATE <author>
10. <perhaps cab> RED WINE = _R ENE outside DWI
11. <venue> NIGHTCLUB = NIGHT TUB outside C L
12. _C _H _U _T _E = CHUTE <way down>
13. (SPEAR + BATTLE)* = BREASTPLATE <armour>
19. <closing bars> OUTROS = O U ←SORT←
22. (N IRISH MP + BANKS)* = BRINKSMANSHIP <risk-taking behaviour>
25. ←DYE← inside HAY = HEYDAY <blooming period>
26. ROMANCE outside AND L = ROMAN CANDLE <one with sparks flying>
32. BORES* = SOBER <abstaining from drink>
33. D_E_ C_L_ + UTTER = DECLUTTER <spruce>
34. <made aware of> ALERTED = A LE RTED
35. (LINE + VEGAN)* = LEAVENING <baking ingredient>
36. <back> ENDORSE = END _ORSE

DOWN
1. <keep company> HOBNOB = HOB NOB
2. <hit song> SINGLE = (...s)SING LE(n...)
3. <time off> HIATUS = (←UTAH← outside I) S
4. <strike> WALLOP = W ALL + OP
5. <burrowing rodent> JERBOA = J_ E_ R_ BOA
6. <medical staff> CADUCEUS = U inside ACCUSED*
7. (A QUID)* + _I_ _R_ _I_ = DAIQUIRI <cocktail>
8. <while> WHEREAS = (WE HEAR)* S
14. <hayseed> RUBE = LUBE, L→R
15. <characteristic of Dust Bowl> ARID = R inside AID
16. K_Y inside TOO = TOKYO <capital>
17. N leaves ←ANIMAL← = LAMIA <a bloodsucking serpent-witch in Greek mythology>
18. (IN COT)* = TONIC <medicine>
20. <spare> THIN = THIN_
21. O + PAL_ = OPAL <gem>
23. (READY BRE_)* = RYE BREAD <cereal product>
24. <storyteller> = ←ARRAN_← ←ROT←
25. <prisoner> HOSTAGE = TAG inside HOSE
27. <confusion> MUDDLE = MULE outside DD
28. <liquid> NECTAR = N + E-CAR outside T
29. <talisman> AMULET = A MULE _T
30. <particular item> DETAIL = RETAIL, R→D
31. A inside GREEN* = ENRAGE <incense>