Each clue prefaced by a number in square brackets provides a cryptic indication of a word (minus a single letter) from a well-known poem (not further defined). Its solution was to be entered without this letter. The missing letters in numbered order give the name of the author:
THOMAS GRAY
Elegy Written in a Country Churchyard
Words: solemn, complain, solitary, anthem, current, tyrant, Cromwell, noiseless, brushing, approach.
Across
1 abated A(ce) + BAT(t)ED
5 calash C<AL(Capone)>ASH
9 unaired double def
10 revel REVE(a)L
11 photon P<HO(use)>TON
12 execrate (River) EXE/CRATE
13 n[O/3]iseless ISLE (anag) in (Loch) NESS
15 onyx NY in OX
17 Gaul GA<U>L
19 agnostic ACTING SO (anag)
23 space age cryptic def
24 grooms G(rand)/ROOMS
26 antem[H/2] MEANT (anag)
27 Cro[M/4]well ORC (rev) + WELL
28 Sharon NORAH���S (rev)
29 tenant TEN<A/N(umber)>T
Down
2 brushin[G/7] B<RUSH>IN
3 t[Y/10]rant T<RAN>T
4 daringly DA(RING/1)ILY
5 curren[T/1] CUR + (child)REN
6 liverwort EVIL (rev) + WORT(h)
7 solit[A/5]ry SOLI + TRY [plural of SOLO]
8 idlers RELIS[H(igh)E(xplosive)]D (anag)
14 solicitor SOL/ICI/TOR
16 long-lost LONG + LOTS (anag)
18 app[R/8]oach AP<PO>ACH(e)
20 Greece GREE(n) + C(hurch of)E(ngland)
21 compl[A/9]in COMPLIN(e)
22 barman B<ARM>AN
25 [S/6]olemn O<L(unar)E(xcursion)M(odule)>N