Across:
1 What the judge is capable of handing down, in as few words as possible (SHORT SENTENCE), to low (SHORT) life? (SENTENCE) (SHORT SENTENCE),
10 Try (HAVE A GO) to use a razor (shave) trimming top (s) (‘shave’ without ‘s’ = HAVE) in olden times (ago = A GO) (HAVE A GO),
11 University (U-) concert hall (National Concert Hall/NCH = -N-CH) welcomes No 1 (-HIT-) (UNHITCH) by Free (UNHITCH),
12 Of course, missing cues (‘of course’ missing ‘cues’ = ofor = ROOF) found on top of the snooker club presumably (ROOF),
13 Restless (ITCHY) in hotel (-H-) in strange (= anagram indicator) city (city = ITC-Y) (ITCHY),
15 Due to get out of used car (‘due’ to get out of ‘used car’ = scar = SCAR) with the lasting mark on the surface (SCAR),
17 Local boozer (SOT) in Minnesota (in ‘minneSOTa’ = SOT),
19 Penny (CO-IN) takes in party (Fianna Fáil = -FF-) (COFFIN) for one of those lifeless figures (COFFIN),
21 Frank (HONEST), Henry (H-) and Oscar (-O-) find the tree house (-NEST) (HONEST),
22 Short (t) role for actor (part) (‘part’ without ‘t’ = PAR-) getting to lose temper (-BOIL) (PARBOIL) in Heat briefly (PARBOIL),
23 Is this what Sisyphus will always do (Greek mythology: Sisyphus forced to eternally roll a boulder up a hill, only to watch it roll back down; so he will always ROLL UP) for a cigarette? (ROLL UP),
25 Half suppressed laugh (TITTER) from Troy (T-) getting beer (bitter) with no head (‘bitter’ without ‘b’ = -ITTER) (TITTER),
27 Bit of advice (TIP) for those three turning up (= reverse indicator) in hospital (in ‘hosPITal’ = pit = TIP),
29 Loosen (UNDO) and dig up (= reverse indicator) segment of dogwood nuisance (segment of ‘dogwoOD NUisance’ = odnu = UNDO),
30 Starting on all sides today (SHORT is on all sides of today’s grid) strapped for cash (SHORT),
31 Fleeces (WOOL) for gents (loo = -OOL) and women (W-) switched (= reverse indicator) (WOOL),
34 Praise (TRIBUTE) for mint (= anagram indicator) butter (butter = TR-BUTE) covering second dish (second ‘dIsh’ = -I-) (TRIBUTE),
35 Irish beach (Irish ‘beach’ = trá = TR-A) going around a (-A-) church (-CH-) near point (East = -E-) (TRACHEA) is perfect for taking the air (TRACHEA),
36 By the sound of it, Kurt (‘Kurt’ = ‘curt’ = SHORT-) is fortified in a steely way (-TEMPERED) (SHORT-TEMPERED) – is that why he’s like a bear with a sore head? (SHORT-TEMPERED).
Down:
2 To divert assets (HIVE OFF) from worker’s home (home of worker bees = HIVE) is not on (OFF) (HIVE OFF),
3 Non-fictional (REAL) rebellious (= reversal indicator) characters from Thermopylae remembered (characters from ‘thermopyLAE Remembered’ = laer = REAL),
4 Oral stimulants (SHORTS) for boxers? (SHORTS),
5 Nothing at all (NOUGHT) in good books (New Testament = N-T) about Hugo (Hugo) Cook (= anagram indicator) (Hugo = -OUGH-) (NOUGHT).
6 Come home without memo (‘come home’ without ‘memo’ = cohe = ECHO) produced by nymph (nymph/spirit called ECHO),
7 Piece of beef (CUT-) from the outskirts of Carrauntoohil (from the outskirts of ‘CarrauntoohiL’ = -CL-) in Ireland (.ie = I-E) (CUTICLE), with the skin, that’s usually removed (CUTICLE),
8 Cuts out (SHORT-CIRCUITS) the current faults (SHORT CIRCUITS),
9 To bridge the pay gap (SHORT-TERM LOAN), close school early (SHORT TERM) to secure finance (LOAN) (SHORT-TERM LOAN),
14 Lively, energetic music (CON BRIO) by Sting (CON-) from Brasilia, the capital (‘Brasilia’ the capital = B-) city in Brazil (-RIO) (CON BRIO),
16 Less coming from suppliers (‘less’ coming from ‘suppliers’ = uppir = RIP UP) to make confetti out of, for instance (RIP UP),
18 Stomach pain (COLIC) produced by short (a) drink (cola) (‘cola’ without ‘a’ = COL-) with endless (e) ice (ice) (‘ice’ without ‘e’ = -IC) (COLIC),
20 Some abandon a programme (some ‘abandoN A Programme’ = NAP) for the rest of the afternoon (NAP),
21 Characters in Whitehall (Characters in ‘wHITehall’ = HIT) or Knock? (HIT),
24 Stable guy (LAD-) having meal (-DISH) (LADDISH) behaves boisterously like one of the boys (LADDISH behaviour),
26 As Yeats saw it, foot (TROCHEE a ‘foot’ with syllables/patterns of rhythm in poetry) of mythological bird (-ROC-) you once (‘you’ once = thee = T-HEE) caught? (TROCHEE),
27 Menace (THREAT) to hare (hare) running (= anagram indicator) (hare = -HREA-) in race (Tourist Trophy = TT race = T-T) (THREAT),
28 Imposter is removed (‘imposter’ is removed/without ‘is’ = mpoter = PRO TEM) for the time being (PRO TEM),
32 The response of the fat cat perhaps (PURR) to jeer from perjurer (to ‘jeer’ from ‘perjurer’ = prur = PURR),
33 Clip of (l) tree nut (‘hazel’ without ‘l’ = HAZE) in Cloud (HAZE).