ACROSS
 1. BASSIST outside O ON = BASSOONIST <woodwind musician
 7. ←M ROD← = DORM <sleeping quarters>
 9. <Herculean> GIGANTIC = GI + G ANTIC
10. OPAL* _MB_ = APLOMB <unconcern>
11. F USE = FUSE <electrical safety device>
12. DINE* + H OVEN = EINDHOVEN <Dutch city>
13. PL + EDGE = PLEDGE <promise>
15. <cross borders> EMIGRATE = EMIRATE outside G_
17. <president> POMPIDOU = POMP + (I DO) + U
19. <hard to find> SPARSE = SPARS + _E
21. HIND [-p]RANCE = HINDRANCE <restraint>
23. <grease> LUBE = _L_U_ + BE
25. <starchy plant> MANIOC = M_A + ←COIN←
26. ←LARGE T NI← = INTEGRAL <important>
27. TUN after S = STUN <floor>
28. <divisive> POLARISING = ←LOP← ARISING

DOWN
 2. A_ D_ I_ E_ U_ = ADIEU <so long>
 3. <sushi ingredient> = →"WEE SEED"←
 4. <recovering> ON THE MEND = (ON THEME) _N _D
 5. (QUESTION NINE C)* AL = INCONSEQUENTIAL <trivial>
 6. _T + RASH = TRASH <nonsense>
 7. <free> DELIVER = ←REVILED←
 8. <thinks> RUMINATES = [.d]RUM IN A TES[.t]
14. <brave person> LION-HEART = (LIAR NOT HE)*
16. <police officer> INSPECTOR = P inside IN SECTOR
18. <payment for the retired> PENSION = PENS + I ON
20. <maintains> ALLEGES = (SEAL + GEL)*
22. REP outside CA = RECAP <summary>
24. BRAN outside W = BRAWN <beef>