Across:
1 In a State where one feels the need to constantly apologise (FULL OF REMORSE) to local awash (local 'awash' = FULL) with free rooms (free rooms) all over the place (= anagram indicator) (free rooms = OF REMORSE) (FULL OF REMORSE),
10 Not swayed (UNMOVED) by a French (‘a’ French = UN-) film (movie) without independent (i) (‘movIe’ without ‘i’ = -MOVE-) director (-D) (UNMOVED),
11 A (-A-) side of tuna (side of ‘Tuna’ = -T-) in sushi (sushi) prepared (= anagram indicator) (sushi = SHI-SU) (SHIATSU) with Japanese pressure treatment (SHIATSU),
12 Bewildered (LOST) by bank’s lobbyist (banks ‘LObbyiST’ = LOST),
13 Frenchman (M-) finding work (-ERG-) close to Marseille (close to ‘marseillE’ = -E) (MERGE) in corporate? (incorporate = MERGE),
15 Running over (FULL) those characters starting for all sides today (FULL on all sides of today’s grid),
17 A number (TEN) of those caught up (= reverse indicator) in fortune-telling (caught in ‘fortuNE-Telling’ = net = TEN),
19 Problem for the electrician (short circuiting = FUSING) as he is not into Feng Shui (‘he’ is not into ‘Feng Shui’ = fngsui = FUSING),
21 Having the freedom musically (RUBATO) in Russia (RU -) to join club (-BAT-) for nothing (-O) (RUBATO),
22 Hasn’t much to say (LACONIC) to The French (‘the’ French = LA-) Connection’s three leading characters (‘CONnections’ three leading characters = -CON-) in charge (In Charge = -IC) (LACONIC),
23 Is jealous of (ENVIES) five (-V-) in Seine doing backstroke (= reverse indicator)? (Seine = EN-IES) (ENVIES),
25 Outlaw (BANISH) bar (BAN-) is (-IS-) near hotel (-H) (BANISH),
27 Starting off (t) on the other side (the other side = them) (‘them’ with ‘t’ = HEM) of The Border? (HEM),
29 You’re on thin ice here (RINK) with bowling team (team in curling / lawn bowling = RINK team),
30 Concealed by Mount Erebus going up (= reverse indicator) (concealed by ‘mounT EREBus’ = tereb = BERET) to a nice cap (Nice/French ‘cap’ = BERET),
31 Part of sombre hotel set up (= reverse indicator) (part of ‘somBRE Hotel’ = breh = HERB) by Rosemary (HERB),
34 Marie Antoinette dropped neat iron (‘Marie Antoinette’ dropped ‘neat iron’ = maiette = TEATIME) at 4pm in the afternoon? (TEATIME),
35 Starter of idli (starter of ‘Idli’ = -I) with any (any) other (= anagram indicator) (any = -YAN-) piece of meat (rib) served up (= reverse indicator) (rib = BIR-) (BIRYANI) in Indian dish (BIRYANI),
36 Contented (FULL) this has nothing (O-) to do with Furlong (-F) taking The Pledge (PROMISE) (FULL OF PROMISE) – potentially, it’s a sign of great things to come (FULL OF PROMISE).
Down:
2 Exposes (UNMASKS) organisation (United Nations Organisation = UN-) to first minister's (first 'Ministers' = -M-) questions (-ASKS) (UNMASKS),
3 Carry a torch for (LOVE) hauling up (= reversal indicator) those inside active volcano (those inside ‘activE VOLcano’ = evol = LOVE),
4 Farsightedness dismissing rashness (‘farsightedness’ dismissing ‘rashness’ = figted = FIDGET) of one who can’t stay still (FIDGET),
5 Flag (ENSIGN) a number of points (East + North = E+N = EN-) for one of the Languages (-SIGN language) (ENSIGN),
6 Don’t include (OMIT) what’s upsetting (= reverse indicator) in testimony (in ‘tesTIMOny’ = timo = OMIT),
7 Serves up (= reversal indicator) a (-A) grape juice (must = -TSUM-) with a (-A-) top slice (top ‘Slice’ = S-) (SATSUMA) of orange (SATSUMA),
8 Can’t get over the remorse and guilt (FULL OF REGRETS), it’s said (= homophone indicator), Hungary no more (‘Hungary no more’ = ‘hungry no more’ = FULL) is for (for) wild (= anagram indicator) (for = OF R-) birds (-EGRETS) (FULL OF REGRETS),
9 Satisfied (FULL) Count (tot = TO T-) got to that man (-HE) from 33 down (‘brim’ = BRIM) (FULL TO THE BRIM) with no room to spare (FULL TO THE BRIM),
14 Get better (RECOVER) in hospital (ER), bringing up (= reverse indicator) (ER = RE-) what you should have got from Insurance Company (-COVER) (RECOVER),
16 Passage (INLET) from sample of chain letters (sample of ‘chaIN LETters’ = INLET),
18 Canal (DUC-T) flowing around area (-A-) (DUCAT) in old capital (old capital/gold coin = DUCAT),
20 Laughing matter (GAS) oddly in Gdansk (oddly / odd letters in ‘GdAnSk’ = GAS),
21 Kid (RIB) raised (= reverse indicator) in Novosibirsk (raised in ‘novosiBIRsk’ = bir = RIB),
24 New Irish (‘new’ Irish = -NUA-) in vessel (vat = VA-T-) heading for uninhabited (heading for ‘Uninhabited’ = -U) (VANUATU) islands in the Pacific (VANUATU),
26 Really cool places (ICE CAPS) in one (I-) top-class (top ‘Class’ = -C-) revolutionary (= reverse indicator) space (space = -E CAPS) (ICE CAPS),
27 Sue leaves free house (‘Sue’ leaves ‘free house’ = freeho = HEREOF) in relation to this (HEREOF),
28 Associate (MEMBER) of bishop (-B-) taken in by viral sensation (meme = MEM-E-) is the first to repent (first to ‘Repent’ = -R) (MEMBER),
32 Extremely unpleasant (vile) reports (= homophone indicator) (‘vile’ = ‘VIAL’) from The Tube (VIAL),
33 Heading for Bugaba (heading for ‘Bugaba’ = B-) close to border (-RIM) (BRIM) in part of Panama (BRIM part of Panama hat).