Surprisingly tame for a DA. Very regional words, however.

Across

1

Opposed to month cycling Caribbean island (7)
ANTIGUA — ANTI (opposed to) reversal (cycling) of AUG (month)

9

Green Party’s leader 4-down (3)
PEA — P (first letter of party) EA (4-down [a head])

10

Writer of the first musical, pared down to include singer (5,6)
TRENT DALTON — T (first letter of the) RENT (musical) DN (down without middle letters) containing ALTO (singer)

11

Keep jogging, run around Tassie reservoir (4,6)
LAKE PEDDER — anagram (jogging) of KEEP inside LADDER (run)

12

A pilot shredded papers to fit (4)
AGUE — A GUidE (pilot) without id (papers)

15

Large foibles seem oddly deficient (5)
OBESE — even letters of foibles seem

16

Wheels in cave hit phone? (9)
BATMOBILE — BAT (hit) MOBILE (phone)

17

Animal made for dry travel no softy at heart! (9)
DROMEDARY — anagram (travel) of MADE fOR DRY without f (middle letter of softly)

18

Shaking about, Trev fixed appliance (1.1.3)
TVSET — TreV without re (about), SET (fixed)

19

NT river delta - spot to kick back (4)
TODD — reversal (to kick back) of D (delta) DOT (spot)

20

(& 5-across) Hot open-ended current eddying, yes? (3-7,3,4)
ONE-HUNDRED PER CENT — anagram (eddying) of H (hot) OPEN-ENDED CURRENT

24

Try to miss catching Tube via complex (4,2,1,4)
GIVE IT A BURL — GIRL (miss) containing anagram (complex) of TUBE VIA

26

Game conundrum partly rejected (3)
UNO — reversal (rejected) of hidden in cONUndrum

27

Knock scoundrel visiting twice? (3-1-3)
RAT-A-TAT — RAT (scoundrel) AT AT (visiting, twice)

28

Tailors deride large top (7)
DREIDEL — anagram (tailors) of DERIDE, L (large)

Down

1

Shell rival camp oligarchs occupied (5)
AMPOL — hidden in cAMP OLigarchs

2

Foals’ past song on album? (5,6)
TRACK RECORD — TRACK (song) RECORD (album)

3

How jigsaw solvers start crumble? (2,2,6)
GO TO PIECES — cryptic def.

4

A pop in the van (5)
AHEAD — A HEAD (pop)

5

Latin type dancing without rush (9)
PATIENTLY — anagram (dancing) of LATIN TYPE

6

Legitimate Spanish royal (4)
REAL — double def.

7

(& 23-down) Attired, wearing fawn? (3,4)
EAT DIRT — anagram (wearing) of ATTIRED

8

Most sensitive Commie upset (offset?) to join X (9)
TENDEREST — TEN (X) reversal (upset) of RED (commie) anagram (off) of SET

13

Advances a sign, cryptically (5,6)
GAINS GROUND — reverse clue of "a sign"

14

AFL won’t stand feller disclosing soft spot (10)
FONTANELLE — aFl wONt sTANd fELLEr, each without outside letters

15

Senior spun guns nestled in Cockney holster (3,6)
OLD STAGER — reversal (spun) of GATS (guns) in OLDER (Cockney holster)

16

Drops remote in empty bucket - a senior moment? (5,4)
BRAIN FART — RAIN (drops) FAR (remote) in BT (outside letters of bucket)

21

Dog hid lead on first escaping shelter (5)
HOUND — H (first letter of hid) on pOUND (shelter, without first letter)

22

Medico counter can produce bodily fluid (5)
DROOL — DR (medico) reversal (counter) of LOO (can)

25

21-down carer, one 15-down? (3)
VET — double def.