Across:
1 Experience anxiety (BITE ONE'S NAILS) in tentatively eating starters ('In Tentatively Eating' starters = -ITE) tucking into rib (rib bone = B- ONE-) and escargots (snails = -S NAILS) (BITE ONE'S NAILS),
10 It’s popular (IN-) on their (their) travels (= anagram indicator) (INHERIT) (their = -HERIT) to be left something (INHERIT),
11 Part of an Indian (BASMATI rice) camp (base) cut short (‘base’ without ‘e’ = BAS-) for runner (-MAT-) on island (-I) (BASMATI),
12 Dealt (SOLD) LSD (LSD) staggering (= anagram indicator) (LSD = S-LD) around job centre (‘job’ centre = -O-) (SOLD),
13 To take off lab coat (‘to’ take off/remove from ‘lab coat’ = labca = CABAL) in intriguing group? (CABAL),
15 Details (INFO) apparent in floodplain forecast (apparent in ‘floodplaIN FOrecast’ = INFO),
17 Naïve leaving vineyard (‘naïve’ leaving ‘vineyard’ = yrd = DRY) in a state that needs irrigation (DRY),
19 Lie cosily (NESTLE) in strife out of self-interest (‘strife’ out of ‘self-interest’ = lneest = NESTLE),
21 A fair amount of (half) drug (half of ‘DRug’ = -DR-) found in fish (tuna = TUN-A) (TUNDRA) in Arctic plain (TUNDRA),
22 Both sides definitely (both sides ‘DefinitelY’ = DY-) manic (manic), wild (= anagram indicator) (manic = -NAMIC) (DYNAMIC) and forceful (DYNAMIC),
23 Soft raw unbleached silk (PONGEE) from Shetland (pony) for the most part (y) (‘pony’ without ‘y’ = PON-), and, for example (e.g.), around (= reverse indicator) (eg = -GE-) Spain (-E) (PONGEE),
25 From what’s been heard you won’t forget this (CATCHY tune) is caught (C-) from yacht (yacht) at sea (= anagram indicator) (yacht = -ATCHY) (CATCHY),
27 Half the characters from 27 down (half ‘KITten’ = KIT) in outfit (KIT),
29 Served up (= reversal indicator) sample of spaghetti meals (sample of ‘spaghetTI MEals’ = time = EMIT) to give out (EMIT),
30 Sun (sun) comes up (= reverse indicator) (sun = -NUS) behind motorway (MI-) (MINUS) takeaway (take away = MINUS),
31 Word of protest (but = B-UT) over ring (-O-) (BOUT) fight (BOUT),
34 Self-absorbed person (EGOTIST) in vain leaves investigation (‘in vain’ leaves ‘investigation’ = estigto = EGOTIST),
35 Twitter (BLATHER) leads to lawyer (Bachelor of Law = BL-) getting heart (heart) trouble (= anagram indicator) (heart = -ATHER) (BLATHER),
36 It’s slightly ridiculous (BIT OF NONSENSE) coming out of Limerick (limerick poem = BIT OF NONSENSE).
Down:
2 His lean (his lean) boss (= anagram indicator) (his lean = INHALES) draws a breath (INHALES),
3 An acid from Ecuadorian (‘an acid’ from ‘Ecuadorian’ = euor = EURO) capital? (capital/money = EURO),
4 You can’t say this about the man downstairs (can’t say the devil is NOT BAD) and that’s fine (NOT BAD),
5 Is responsible for underground movement (SUBWAY) going back (= reversal indicator) by public transport (bus = SUB-) to Washington (-WA-) on Fourth of July (fourth of ‘julY’= -Y) (SUBWAY),
6 Covered up by global society (covered up by ‘globAL SOciety’ = ALSO), to boot (ALSO),
7 Made money from working (-EARNED) behind (= position indicator) novice (learner = L-) (LEARNED) and academic (LEARNED),
8 Bandits (bandits) at sea (= anagram indicator) (bandits = BITS AND) with guns (PIECES) (BITS AND PIECES) and assorted items (BITS AND PIECES),
9 What goes on four feet in the morning, two feet at noon, and three feet in the evening? (The Sphinx’s riddle = BIT OF A MYSTERY) That’s puzzling! (BIT OF A MYSTERY),
14 It’s a job for a criminal (BREAK-IN) to bring to heel those from a stable environment (BREAK-IN horse),
16 Loses the head (w) with one of those carrying a torch (‘welder’ without ‘w’ = ELDER) for patriarch (ELDER),
18 Canal (DUC-T) flowing around area (-A-) (DUCAT) in old capital (old capital/gold coin = DUCAT),
20 Honey eater dismisses another (‘honey-eater’ dismisses ‘another’ = yee = EYE) viewer (EYE),
21 The odd twitch (the odd ‘TwItCh’ = TIC) or peculiarity (TIC),
24 A (-A-) leading investor (leading ‘Investor’ = -I-) to rip off (-ROB-) in Ulster (NI = N-I) (NAIROBI) city? (NAIROBI),
26 Type of gear (CLOTHES) he’s (-HES) after (= positional indicator) – the clumsy fool (CLOT-) (CLOTHES),
27 Small foxy type (KITTEN) of gear (KIT-) is half rotten (half ‘rotTEN’ = -TEN) (KITTEN),
28 Old city (-UR-) bishop (-B-) taken in by shady type (T-AN) (TURBAN) covering the head (TURBAN),
32 Finishes all the dishes – spaghetti, veal, burrito (finishes all the ‘disheS – spaghettI, veaL, burritO’ = SILO) from food store (SILO),
33 Third rate (third ‘raTe’ = T-) drink (-ALE) (TALE) and whopper? (TALE).