I solved this with the help of a Google friend (Howard Trickey — thanks!). Unlike a typical Listener, we cracked the theme well before solving all the clues (with the help of a certain well-known search engine and the terms “Christmas Carol beauty” we found http://www.carols.org.uk/we_three_kings_of_orient_are.htm).
The central column reads: “OF ORIENT ARE” — so, your job was to have submitted a clue for WE THREE KINGS. I didn’t.
Only thing that I’m not sure about is the wordplay for KEENLY, and a slight uneasiness about LEONE (perhaps bad clue?). I’ve left the original clues with the division between the two halves.
1, 33 Crummy but popular syce dodging round both ends of horse / succeeded with clasp for prop to increase height (6, 6) CHEESY - (syce, h[orse]e)* / S,CATCH - it’s a stilt
6, 32 Object in test: it’s chic / to chat in French about druggie – one’s motivational (6 6) TR(END)Y / CA,USER - two defs + wordplay since CAUSER means to chat in French as well.
10, 31 Mexican dish cheers man / like fish that’s not old inside or distended (6, 6) TA,MALE / AS,TR[o]UT - distended
11, 30 Having left a long time going over theme of this puzzle / one’s almost late producing brainwave maybe (4, 4) NOE,L - rev(eon) and it’s the puzzle’s theme I guess / I,DEA[d]
14, 29 Little fish in cove snapping line / goes swimming for small inlets (4, 4) B(L)AY - a small fish / GEOS = goes* – gullies, creeks (close enough to small inlets I guess?)
15, 26 E.g. acute tonsillitis, a feature of Penang in autumn / monsoon by the sound of it, is prevalent (6, 6) ANGINA - any inflammatory affection of the throat / REIGNS=”rains”
16, 25 Oily paste: dilute one including a / snort by the medium of beer dosed with heroin (6, 6) TAHINA - it’s an “oily paste” – T(A)HIN,A / IN(H)ALE
17, 24 Top golfer in tangle producing phrase that threatens / people beside start of hole – he’ll receive counselling (6, 6) OR (ELS)E - ORE (tangle) in Ernie ELS / MEN,TEE
20, 23 Sign of turn and A. Nel’s bowling: open / batting (with turn) very quietly – that is, one waited for the tea period! (6, 6) UNSEAL - (U, A. Nel’s)* means “open” / NI,PP,IE - rev(in=batting), she’s a Lyons Corner House tea lady.
1 STAR OF NIGHT
2, 28 Part of window leading turned out / almost ineffectual – common sense required (4, 4) CAME – double def “turned out” and a lead rod for framing a pane in a leaded window / NOUS[e]
3, 22 Eating on the move, whereby one enters / a legit ramble or trudge in the highlands (6, 6) INGATE* / TAIGLE* - Scots trudge
4, 27 E.g. Cameron or Clegg? Not mine – one follows / Brown ultimately; he’s oddly tender (4) CL[egg],AN - egg = “a bomb or mine (sl)” / [Brow]N,ESH* - “delicate in one’s health”
5, 26 Calculator: one getting into basics / cuts hard exercises with sums – introductions only required (4, 4) AB(A)C - where ABC are the “basics”, def is nomogram which is a kind of calculator. I hope / HEWS - “cuts” - initial letters
6, 21 Above us tomb of stone or rock rose / sharply in the air but airless – essential to go round it (6, 6) CIST,US - it’s a kind of rock-rose and CIST is a stone tomb / I want this to be KEENLY. Maybe somehow ‘k(it)e’ is involved?
7, 19 Restrained in case (being old), I’ll / progress very little in a foxtrot, say (7, 7) ST(ILL)ED - I’ll in STED (archaic case) / A,D(V)ANCE
8, 13 Fantastic vin: we hope caller’s seen in it / what’s repugnant in bubbly asti for Frogs etc (9, 9) VIEWPHONE - (vin: we hope)* / S(ALIEN)TIA - order including frogs and toads
9 ROYAL BEAUTY
12, 18 Having taken a bit of a kip in a way woolly / Indra wandering round East did his stuff! (6, 6) LAN(AT)E - means “woolly”, a kip is Laotian currency consisting of 100 ATs (misled by NAPPED - (double def)/ RAINED - E in Indra* – &lit since Indra is Hindu god of rain.
A Turbulent age in aeon that’s transformed tropical America (7) NEOGAEA - (age, aeon)*, means “tropical America”: entered: OEAGEAN
B Nets catching odd bits of flat coral types (7, 2 words) SEA (F[l]A[t])NS - seans = seines: entered: FSASNEA
C Drains steamer, power gone off inside (7) S(P,ONGE*)S - entered: OSSEPNG
D Row breaking out in court (7) RUCTION* - entered: RUCNIOT
E Wild idiot clutching numberless Kalashnikov in gang robbery (7) D(AK)OITI - AK in idiot* – entered: IKIAODT
F Supplies new work force for regressive authority in Mersey’s centre (6) R(EMAN)S - rev(name) in [me]RS[ey] – entered: EMNARS
G Some African currency units following the French (5) - LE,ONE - standard monetary unit of Sierra Leone thus “some African currency” — i’m a little concerned that plural units is ONE? – entered: NELOE. Seems like the clue is really indicating LEONES?
H Top footballer (4) BEST - ref. George BEST – entered: TBSE
I Purée folded in remoulade (3) DAL - hidden rev – entered: ALD
J, K Sports facility forming part of Centre Court (3) REC - hidden - entered RCE