Across
Pair winning almost immediately? (6)
I haven't cracked this one yet — but Times for the Times have:
PR(pair) and ON TOP(winning) minus the last letter
Married woman or country boy featured in curse (7)
Old piano delivered before time for stage performance (5)
Forswearing group full of English hypocrisy (9)
I haven't cracked this one yet — but Times for the Times have:
RING(group) containing E(English), CANT(hypocrisy)
A boy given time becomes VIP (9)
Instrument costing nothing no good? Return it! (5)
I haven't cracked this one yet — but Times for the Times have:
GRATIS(costing nothing) minus G(good) reversed
Payment slashed? (4)
Remarkable chum hugging female and old blokes (10)
I haven't cracked this one yet — but Times for the Times have:
PAL(chum) containing HEN(female) and O(old), MEN(blokes)
Trade ad is out to catch people ultimately, offering essential items? (10)
I haven't cracked this one yet — but Times for the Times have:
anagram of TRADE,AD,IS containing the last letter in peoplE.
One church had to be decorated (4)
I haven't cracked this one yet — but Times for the Times have:
I(one), CE(church), ‘D(had)
Projection of sentimental stuff suiting the nobs? (5)
I haven't cracked this one yet — but Times for the Times have:
CORN(sentimental stuff), U(suiting the nobs). Got this from wordplay. Since there’s a bunch of comments about this answer, I’ll add my two cents. Cornu is Latin for horn, and in English means either a horn or a hornlike pattern in nature, so a projection. More commonly found as the first part of CORNUCOPIA, horn of plenty. It might be more common in the USA, but CORN or CORNY meaning sentimental or trite came quickly to me.
What makes Oxford look bright? (9)
Officer studies information schematically presented (9)
Piece of cloth I found behind organ (5)
I haven't cracked this one yet — but Times for the Times have:
I after LUNG(organ). Another from wordplay – last appeared in a Times puzzle in 2015
Duck is some swimmer, seriously! (7)
Hearing that is very irritating (6)
Down
Publicity bod hurried round about and was successful (9)
I haven't cracked this one yet — but Times for the Times have:
PRO(Public Relations Officer, publicity bod) then SPED(ran) surrounding RE(about)
Series of deliveries managed but took too long (7)
Table with a flower still to be put up outside (6)
I haven't cracked this one yet — but Times for the Times have:
A, PO(flower) with YET(still) reversed surrounding. Another from wordplay, and a search of the site shows it popped up in two Jumbos in 2016 and 2012, but has not been seen before in a daily.
Fellow consuming cold mineral (5)
Solitary advance amount of cash reported (8)
Bird with leg in something mouldy (7)
Country boy with change of direction finally (5)
I haven't cracked this one yet — but Times for the Times have:
NIGEL(boy we’re only making plans for) with L changing to R
Bishop back, having embraced the brief time out? (8)
I haven't cracked this one yet — but Times for the Times have:
B(bishop) and REAR(back) containing THE
Ignore heartless nut spouting gas (8)
I haven't cracked this one yet — but Times for the Times have:
anagram of IGNORE and NuT minus the central letter
Heather coming across snake and running (9)
A revolutionary socialist restricts fair person who'd make small changes (8)
I haven't cracked this one yet — but Times for the Times have:
A then RED(socialist) reversed containing JUST(fair)
Problem gripping Rex in a state (7)
I haven't cracked this one yet — but Times for the Times have:
SUM(problem) containing R(Rex), IN, A
Drink? Church worker imbibes one — and another one (7)
I haven't cracked this one yet — but Times for the Times have:
CH(church), ANT(worker) containing I(one) and then another I
Bird losing tail, pinned down by wood and stone (6)
A court beset by a hundred and one plants (5)
Black farm building time's forgotten (5)
I haven't cracked this one yet — but Times for the Times have:
STABLE(farm building) minus T(time)
Type letters or click words in the clue