Lots of nice clues in this puzzle.
I spent a lot of time looking at 21A but still can't work that one out. Of the other clues, I liked 4D, 23D and 12A.

| ACROSS | ||
| 9 | ATROPHY |
First-class memorial in decline (7)
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A(=first class) + trophy(=memorial) |
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| 10 | EVIDENT |
Clear papers to enter sports contest (7)
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Id(=papers) in event(=sports contest) |
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| 11 | RADAR |
Locating apparatus right next to drama school (5)
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R{ight} after RADA(=famous drama school) |
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| 12 | OPEN COURT |
Promote saving time – choose cases where trials are accessible (4,5)
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Opt(=choose) around(=cases) (encour[age])(=promote with age=time removed) |
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| 13 | NITRATE |
Starting over without covering earth in fertiliser (7)
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[S]tartin[g]< + e{arth} |
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| 14 | BREATHE |
About to wash trousers and relax (7)
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Bathe(=to wash) around(=trousers) re(=about) |
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| 15 | ALPHA PARTICLE |
Appear chill at parties – it might cause a harmful reaction (5,8)
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(Appear chill at)* |
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| 21 | PLACEBO |
Time and time again leave bottle cap off fake medicine (7)
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Don't get this |
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| 23 | MIRACLE |
Surprising event coming primarily after God breaches distance (7)
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(Ra(=Egyptian sun god) + c[oming]) in(=breaches) mile(=distance) |
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| 25 | NEFARIOUS |
Are fusion bombs immoral? (9)
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(Are fusion)* |
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| 26 | GAMMA |
Mum accompanying school’s third grade (5)
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Ma(=mum) after gam(=a word for a school of whales). Gamma is the third letter of the Greek alphabet, so sometimes used to mean third best. |
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| 27 | EMOTION |
Put back book about following one’s passion (7)
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Tome<(=book) + (on(=about) after I(=one)) |
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| 28 | EXTRACT |
Take out additional vacuous comment (7)
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Extra(=additional) c[ommen]t |
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| DOWN | ||
| 1 | WARRANT |
Authorisation to go on supporting struggle (7)
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Rant(=go on, as in "go on at someone") after war(=struggle) |
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| 2 | CREDIT |
Acknowledgement of direct shot (6)
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Direct* |
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| 3 | APPROACH |
Program fish to draw near (8)
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App(=type of computer program) + roach(=type of fish) |
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| 4 | ZYGOTE |
Ultimate couple turned up and received drug for successful conception (6)
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Yz<(=ultimate two letters of the alphabet) + got(=received) + e{cstasy}(=drug). In biology, a zygote is a fertilised egg cell. |
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| 5 | REMEMBER |
Pay tribute to one of the Sappers? (8)
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CD/DD. RE member(=one of the sappers i.e. member of the Royal Engineers) |
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| 6 | CIRCLE |
Ring some friends, maybe (6)
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DD |
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| 7 | REBUTTAL |
Statement denying actual bottom-pinching (8)
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Real(actual) around(=pinching) butt(=bottom) |
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| 8 | STUTTER |
Second person expressing disapproval in hesitant speech (7)
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S{econd} + tutter(=someone tutting) |
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| 16 | LEAP FROG |
A golfer played entertaining power game (4-4)
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(A golfer)* around p{ower} |
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| 17 | PROFOUND |
Deep division in a stone, for climbing inside (8)
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Pound(=division of a stone, as in 14 pounds make a stone) around for< |
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| 18 | IRRIGATE |
Mad doctor enters water (8)
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Rig(=doctor as a verb) in irate(=mad) |
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| 19 | SPANNER |
One going over what mechanic might need (7)
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DD |
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| 20 | PENALTY |
Fine plan yet to unfold (7)
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(Plan yet)* |
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| 22 | EARWIG |
Secretly try to catch bug (6)
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DD |
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| 23 | MASTER |
Guide beginner away from debris going up river (6)
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[J]etsam<(=debris) + r{iver} |
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| 24 | COMBAT |
Engagement from search party ignoring the odds (6)
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Comb(=search, as in "comb the area") + odd letters removed from [p]a[r]t[y] |
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I think 21a is an anagram of BOTTLE CAP without the two T’s
An enjoyable puzzle with some very tight cluing. Some of the container/insertion clues were quite tricky to spot. And I spent far too much time trying to think of an illness or similar instead of ALPHA PARTICLE. LEAP FROG is delightful.
Thanks both