ACROSS
 8. <first-born> ELDEST = _E _L _D _E _S _T
 9. <Man's here> IRISH SEA = IRIS HE'S* + A
10. <criticise> REPROACH = REACH outside PRO
11. <unconcerned> CASUAL = CA [-u]SUAL
12. ←RUE← O = EURO <Malta's capital>
13. (CHARIOT IS)* L = HISTORICAL <period-authentic>
16. ←AH← + IT _I_AN = HAITIAN <Toussaint Louverture?>
18. <beg> BESEECH = (S E) inside BEECH
20. R POLE* + ADDER = ROPE LADDER <climbing gear>
24. _T RIO = TRIO <threesome>
25. <something explosive> ETHANE = _E THANE
27. PATCHING* = NIGHTCAP <sleepwear>
28. <problem in hearing> TINNITUS = TIN NIT + US
29. <waste> ORDURE = D_ inside OR URE

DOWN
 1. ALL + ←_A_I_U_ L_E_← = ALLELUIA <praise for God>
 2. (ROB* + T) inside BEETLE = BEER BOTTLE <evidence of drinking>
 3. TT inside AA C + H = ATTACH <to join>
 4. ←IN← CHE'S = NICHES <hidey-holes>
 5. <make public> DISCLOSE = DISC + LOSE
 6. <some resistance> OHMS = _O_ + HMS
 7. <state> NEVADA = NDA outside EVA
14. <tavern> INN = IN _N
15. <being incompetent> INEPTITUDE = I (NEED IT PUT)*
17. A MARE + ←OTT← = AMARETTO <liqueur>
16. "BUY" = BYE <free pass>
19. CHI VARY outside _L = CHIVALRY <gentlemanliness>
21. <get> OBTAIN = ←(.i)NI AT BO(d.)←
22. <European> DANISH = DAN IS H
23. REG ROW = REGROW <come up again>
26. ←(.e)EN CA(r.)← = ACNE <complaint>