Across:
1 Where one is taught to take the lead (SCHOOL OF DRAMA) in the nursery with the play-actors (SCHOOL OF DRAMA),
10 Twist (CONTORT) fleece (CON-) – it has the potential to be a suit? (-TORT / law suit) (CONTORT),
11 Hasn’t much to say (LACONIC) to The French (the = LA-) Connection’s three leading characters (‘connections’ three leading characters = -CON-) in charge (-IC) (LACONIC),
12 Fail to mention (OMIT), took aim? Missed oak! (‘took aim’ missed/without ‘oak’ = toim = OMIT),
13 One of the overseas (‘overseas’ = ‘oversees’ = chairs = CHAIR) reports (= homophone indicator) is on the committee (CHAIR),
15 The Verve (verve/gusto = BRIO) in Brazilian capital (‘Brazilian’ capital = B-) city in South America? (-RIO) (BRIO),
17 Troublemaker (IMP) promises to cut roses (‘promises’ to cut ‘roses’ = pmi = IMP),
19 A vital (a vital = LATVIA) building (= anagram indicator) in Eastern Europe (LATVIA),
21 Sounds like (= homophone indicator) it’s over a ship (‘a sail’ = ‘ASSAIL’) for attack (ASSAIL),
22 27 down (‘school’ = SCHOOL-) is headstrong (head ‘strong’ = -S) (SCHOOLS) in trains (trains/teaches = SCHOOLS),
23 Elder statesmen to get rid of the smart set (‘elder statesmen’ to get rid of the ‘smart set’ = eldeen = NEEDLE) for Spike (NEEDLE),
25 Any living thing (animal = LAMINA) can be raised (= reversal indicator) on a thin plate of rock (LAMINA),
27 Model (SIT) consumed by revolutionary (= reversal indicator) Britishness (consumed by ‘Britishness’ = tis = SIT),
29 Footsteps in the snow leads (‘footsteps in the snow’ leads = FITS) to explosions, in a comical sense (FITS of laughter)
30 Strike terror into (SCARE) school (S-) management (-CARE) (SCARE),
31 Sounds like (= homophone indicator) the craic (‘craic’ = ‘crack’ = SHOT) coming out of the bar (SHOT drink),
34 Split (split/tear = RIP-) institute (-I-) sets up (= reversal indicator) one (one = -ENO) (RIPIENO) musical group (musical group/instruments = RIPIENO),
35 A boring type (DRILLER) by tiny stream (-RILL-) in Germany (German domain = .de = D-E-) near river (-R) (DRILLER),
36 Group of gamblers (gamblers/poker SCHOOL) in favour of Brexit (LEAVERS) (SCHOOL LEAVERS), looking for a new course to take, to a degree (SCHOOL LEAVERS).
Down:
2 Fraud (CON-) linked to half a dozen (6 = -VI-) goes to court (-CT) (CONVICT) – one of them is put away (CONVICT),
3 Tips on back of envelope (tips ‘on back of envelope’ = OBOE) by one of those down the pit (OBOE in orchestra pit),
4 Lost (L-) desire (-ITCH-) for one (-I) (LITCHI) Chinese fruit (LITCHI),
5 Knocked over (= reversal indicator) Tablet (pill = -LLIP) in opening (‘in’ opening = -I-) taking top from flask (top from ‘flask’ = F-) (FILLIP) for a stimulus (FILLIP),
6 Head off (t), of course (‘track’ without ‘t’ = RACK), with one of the lambs (RACK of lamb),
7 Gold-digger (MINER-) from Virginia (-VA) (MINERVA) is a goddess (MINERVA),
8 Classy outfit (SCHOOL UNIFORM) seen swimming in the water (SCHOOL of fish) the same way throughout (UNIFORM) (SCHOOL UNIFORM),
9 They’re known for giving lessons (SCHOOLMASTERS) to 16th century Venetian artists (Venetian SCHOOL of artists) and Dutch artists in the 17th century (Dutch -MASTERS) (SCHOOLMASTERS),
14 Rounds (AMMO-) knocked back (= reversal indicator) in (in = -NI-) Central (a) Bar (central ‘bar’ = -A) (AMMONIA) for the gas? (AMMONIA),
16 Seating option (AISLE seat) and key (music key A-) for Capri (-ISLE) (AISLE),
18 Composition (ESSAY) of wild (= anagram indicator) seas (seas = ESSA-) at the end of January (at the end of ‘January’ = -Y) (ESSAY),
20 Some of the name-calling (some of the ‘name calling’ = e ca) upset (= reversal indicator) (eca = ACE) expert (ACE),
21 Leave peas out of paellas (leave ‘peas’ out of ‘paellas’ = lla = ALL) and the whole enchilada (the whole enchilada = an idiom for ALL),
24 It’s the subject of debate (-TOPIC) after (= position indicator) community (European Community = EC-) (ECTOPIC) produced a medical case of findings in an abnormal place (ECTOPIC),
26 Turns up (= reversal indicator), most of (y) the broadcast (‘relay’ without ‘y’ = rela= -ALER-) on hero (-H-) from Ulster (NI = IN-) (INHALER) is perfect for having a breather (INHALER),
27 Drill (SCHOOL), for starters, for a number of sides today (SCHOOL on four sides of today’s grid),
28 Tenor (T-) is bad mannered (rude = -RUD-E) about key (music key -G) (TRUDGE) produced by a giant, by the sound of it going walkabout (walk heavily = TRUDGE),
32 Alternates from personal estate (‘alternates’ from ‘personal estate’ = peso = PESO) to Latin American capital (PESO),
33 Bookie verified deposit of (‘bookie verified’ deposit in = KIEV) capital (KIEV).