Across
Heave sledge carrying bags (7)
Refuse to massage out of work clergyman (7)
I haven't cracked this one yet — but Fifteensquared have:
RUB + BISHOP less OP (work)
A tiny bit left in jar (4)
I haven't cracked this one yet — but Fifteensquared have:
L in JOT (tiny bit). This is one of several clues in the puzzle where the insertion seems to be the wrong way round: you expect L in a word for jar, but it’s actually “a tiny bit” with “left in”.
Water bear is slow to hear order (10)
I haven't cracked this one yet — but Fifteensquared have:
“Tardy” + GRADE ([put in] order).
Drink exotic pop in Arabian city (6)
Anne modelled with a lot of babies (8)
Do a jig in new building next door (9)
I haven't cracked this one yet — but Fifteensquared have:
(DO A JIG IN)*
It emerges after Charlie turned over shells (5)
I haven't cracked this one yet — but Fifteensquared have:
C[harlie] + reverse of AMMO. The Comma is a type of butterfly (named after comma-shaped markings on its wings), which could be said to “emerge” from its chrysalis.
Run out of paper to light fire (5)
Turn detective — many removed from gambling game (9)
Expecting Parliament's first ruling (8)
Rhyme "popper" with "propper"? (6)
I haven't cracked this one yet — but Fifteensquared have:
W[ith] EASEL (a “propper”), and a reference to the nursery rhyme “pop goes the weasel”
This material absorbs bandleader and court trainee (6,4)
Upright appearance of Mrs Grundy? (4)
A very little insect trapped in tin (7)
Each season is embodied in songbook (7)
Down
Squeaky clean son departs (7)
Standing order for dress (3,2)
Duck or swallow? (3,4)
Concert outside society wedding (6)
It's sung by woman in the altogether (9)
Cut identity card with letter opener or sword? (7)
Delivery for sister — summons to give up third letter (13)
Forced to deal big blow (9)
Execute salesman returning with document (7)
See 21
20d
Plaintive animal sounds heard in area of common comparison (3,4,2,5)
Snack with small bodybuilder, once (6)
Call to eject England produces outrage (5)
Type letters or click words in the clue