ACROSS
 1. CONS I STEN T = CONSISTENT <without breaks>
 9. <satellite> ORBITER = _R inside OBITER
11. A Y after ←RX← = X-RAY <medical procedure>
12. <Australian woodlouse> SLATER = S LATER
14. "EYE SUP" = ICE UP <start to freeze>
16. TOUPEE - U = TOPEE <pith helmet>
17. DIVO_* = VOID <not legally binding>
18. PAT IS (_E_ inside SIR) = PATISSIER <baker>
20. EACH after R = REACH <leap of logic>
22. RET ←OR← = RETRO <in again>
24. <US board game> PARCHEESI = PAR "CHEESY"
27. ←_A_E_ R_A_← = AREA <neighbourhood>
28. <hubristic> PROUD = PRO U_D
30. <hospitality business> MOTEL = MO TEL
31. <fair> BLONDE = NOBLE* outside D
32. <African kingdom> PUNT <Old Irish coinage> PUNT <rivercraft>
33. OS outside LUMPY* = OLYMPUS <mountain>
34. <play> THE TEMPEST = T + THEME* P_ E_ S_ T_

DOWN
 1. <one splits the bill> CO-STAR = COSTA R
 2. <deck> ORLOP = RL OP after _O
 3. <place> SITE = "CITE"
 4. (BELIEVES CAR)* = SERVICEABLE <in working order>
 5. TRIES, O←E = TRIOS <music groups>
 6. <cuts out> EXCISES = EXORCISES - OR
 7. <more strained> TAUTER = TATER outside U
 8. (.s)HY PER(s.) = HYPER <unusually energetic>
10. TEE _T _H = TEETH <enforceability>
13. A P RAT outside PA = APPARAT <communist organisation>
15. [-s]EDITION = EDITION <issue>
19. <build up> ACCRETE = AC + CRETE
21. EA + TOUT = EAT OUT <aren't responsible for mess?>
22. <return> REPLY = RELY outside P_
23. <most rum> ODDEST = (TODDIES - I)*
24. <interrogates> PUMPS = U MPS after P
25. <Spartan slave> HELOT = ←(.s)TOLE H(o.)←
26. _K _U _D US = KUDUS <antelope>
29. <play boisterously> ROMP = ←PM OR←