ACROSS
 1. <unfairness> INJUSTICE = INCITES* outside JU_
 6. <seal> SIGIL = ←LI GIS←
 9. <church service> VESPERS = (.l)VES PERS(o.)
10. <adult> GROWNUP = W_N inside GROUP
11. <throat inflammation> TONSILLITIS = TONS ILL (IT IS)
12. R_ H_ O_ = RHO <letter from abroad>
13. <the King> ELVIS = EL V I S_
15. _EN_ CLERIC* = ENCIRCLE <ring>
18. TEENAGER* = GREEN TEA <matcha?>
20. <herb> THYME = "TIME"
22. <higher education> UNI = UNI[-t]
23. <churchgoer> PARISHIONER = PARIS HI ONE _R
26. ROUT after _AIN_ = RAIN-OUT <cancelled game>
27. EROTIC* + _E = COTERIE <clique>
28. <Frenchman who painted> MANET = ←(TEN AM)←
29. LUST* outside TRIES = SULTRIEST <most sexy>

DOWN
 1. <those able to attend> INVITEES = (II outside NV) TEES
 2. J AS ON = JASON <Greek hero>
 3. <sort> SPECIES = _I_E_ inside SPECS
 4. INSOLENT outside V = INSOLVENT <bankrupt>
 5. WEIGHT - W = EIGHT <cube>
 6. SNOOPS* + R = SPONSOR <finance>
 7. RALLY after GENE = GENERALLY <in most cases>
 8. ←PAL← + TOP = LAPTOP <computing device>
14. <red> VERMILION = LION after VERMI[-n]
16. <traditional> CLASSICAL = C LASSI C A L
17. (ENTER RIO)* = REORIENT <get one's bearing back>
19. EX PILOT* = EXPLOIT <adventure>
20. TWIST ←RE← = TWISTER <party game>
21. QUO[-i] RUM = QUORUM <requirement for business meeting?>
24. "RIGHTS" = RITES <customs>
25. NEVER, R← = NERVE <daring>