There was a pleasingly old-fashioned feel to this puzzle, I felt; plenty of double definitions, which seem to have dwindled in popularity since I was a lad. Very nice clueing throughout – thank-you, Mudd.
ACROSS
1. REPAST S [small] within reversal of taper [become thinner]
4. CHOP-CHOP Repetition of chop [hack]
9. PRIORY Rio [port city] within pry [nose]
10. SAINTDOM Sodom [one of the sinful Biblical cities of the plain] with o [naught] replaced with aint
12. AIRSPEED Anagram of see rapid
13. CHANGE Double definition
15. EAST (B)east [animal]
16. DRAWING Double definition
20. TREADLE Anagram of altered
21. BALL Double definition, alluding to ‘spot the ball’ newspaper competitions
25. ALPINE Pin [leg] within ale [drink]
26. FOOTWEAR O [round] + anagram of two within fear [suspect]
28. BARITONE It within baron [peer] + E [English]
29. ADJOIN A DJ [one who plays records] + o [zero, nothing] + in [popular]
30. TETHERED Hidden in voTE THE REDneck
31. SONNET Reversal of nos(e) + net [score a goal in football]
DOWN
1. REPEATER Double definition
2. PRIMROSE Rim [border] within prose [plain words]
3. SCRAPE Double definition
5. HEAL Sounds like heel [part of the foot]
6. PENCHANT Pen [female swan] + chant [cry]
7. HIDING Double definition
8. PAMPER (Exa)m within paper [test]
11. HEARSAY Ears [organs] within hay [grass]
14. SWALLOW Double definition
17. BRUNETTE Net [catch] within brute [animal]
18. CAMEROON O(rder) within Cameron [our beloved PM]
19. CLARINET In [hip, fashionable] within claret [blood]
22. RABBIT R [runs] + a + b-bit [l-little]
23. SPIRIT Double definition
24. STUDIO Stud [playboy] + I + o [zero, love]
27. ONCE (B)once [head]
The cryptic crossword world is full of enjoyable not too tricky crosswords today and I enjoyed this one greatly. Thanks to Mudd and Ringo too.