I made heavy weather of this, probably down to the anagrams, and took 13 minutes. I hope it’s just me as, on review, I can’t see why I got held up.
I've had a bit of a tussle with the new livejournal editor. I can't seem to do anything with the extra spaces so let me know if it's a problem (for next time).
ACROSS
During prohibition, show disapproval of primate (6)
BABOON - during prohibition (BAN), show disapproval (BOO).
4. Successful striker, one making one's mark? (6)
SCORER - double definition.
9. Funny reason to embrace democrat in the end, US politician (7)
SENATOR - anagram (funny) of REASON embracing democra(T).
10. Sovereign added to rotten bid (5)
OFFER - sovereign (ER) added to rotten (OFF).
11. Star element (4)
LEAD - double definition.
12. Cautious individual, we hear? (8)
DISCREET - homophone of individual - discrete.
14. Tart up for this fantasy? (3,2,3,3)
PIE IN THE SKY - a tart (PIE) up (IN THE SKY).
18. Carving of mahogany for Scottish festival (8)
HOGMANAY - anagram (carving) of MAHOGANY.
20. Mix porridge (4)
STIR - double definition.
22. Hope last seen of apparent decay (5)
TRUST - as in ' I trust/hope you had a good time' - last seen of apparen(T), decay (RUST).
23. Ultimately, prerogative mine to assume the nickname (7)
EPITHET - ultimately prerogativ(E), mine (PIT) to assume (take inside) the (THE).
24. See anything but frozen water (6)
NOTICE - anything but frozen water (NOT ICE).
25. Drink reserved, also bottled (6)
SHANDY - reserved (SHY) bottling also (AND).
DOWN
1. Subtle changes in old garment (6)
BUSTLE - anagram (changes) of SUBTLE.
2. Girl, one after boy from southern Asia (7)
BENGALI - girl (GAL) and one (I) after boy (LAD).
3. Written in memo, a thoughtless promise (4)
OATH - written in mem(O A TH)oughtlesss.
5. Little time invested in needlework, note (8)
CROTCHET - little time (T) invested in needlework (CROCHET).
6. Arm in error, if leg! (5)
RIFLE - in erro(R IF LE)g.
7. Something unusual I try to change under artist (6)
RARITY - anagram (to change) of I TRY underneath artist (RA).
8. Problem brewing artisan beer (11)
BRAINTEASER - anagram (brewing) of ARTISAN BEER.
13. Massive caper briefly following concert (8)
GIGANTIC - caper (ANTIC) following concert (GIG). Not sure why 'briefly' is in here. Any ideas anyone?
15. Desire in boy to see galley (7)
KITCHEN - desire (ITCH) inside boy (KEN).
16. Wrong keeping shed enclosed (4,2)
SHUT IN - wrong (SIN) holding shed (HUT).
17. Quite alluring (6)
PRETTY - double definition.
19. Noise coming from good little piggy? (5)
GRUNT - good (G), little piggy (RUNT of the litter). Partial &lit where the word play is also necessary to provide the definition.
21. Some crockery I’d upset: don’t say a word! (4)
DISH - I’d upset (DI), don’t say a word (SH).