Across:
1 Brief (SHORT AND SWEET) impolite type (SHORT) as well as (AND) those in 30 across ('sweet' = SWEET) (SHORT AND SWEET),
10 Hotel (H-) mysteriously (= anagram indicator) bank (Allied Irish Banks = AIB = -IBA-) on Greek character (Greek character/alphabet = -CHI) (HIBACHI) doing the work of a small barbecue (HIBACHI),
11 Hagiographer dismisses Grieg (‘hagiographer’ dismisses ‘Grieg’ = haoaphr = PHAROAH) as a member of old royal family? (PHARAOH),
12 Size up (RATE) edges of turned up (= reverse indicator) Eton collar (edges of ‘ETon collAR’ = etar = RATE),
13 It’s scarce (SHORT) starting for all sides today (SHORT on all sides of today’s grid),
15 Mix (STIR) of cast iron sample (‘caST IRon’ sample = STIR)
17 Unfinished (e) museum (‘tatE’ without ‘e’ = TAT) of shoddy jewellery (TAT),
19 Unique (ONE-OFF) old revolutionary (Wolfe Tone) loses the head (t) (‘Tone’ without ‘t’ = ONE -) with posh guy (toff) needing no introduction (t) (‘Toff’ without ‘t’ = -OFF) (ONE-OFF),
21 Highwayman (BANDIT) Bar (BAN-) is for returning (= reverse indicator) heads, teachers, instructors, disciplinarians? (heads ‘Teachers Instructors Disciplinarians’ = tid = -DIT) (BANDIT),
22 Head of cauliflower (head of ‘Cauliflower’ = -C-) in potato (potato) soup (= anagram indicator) (potato = TOP-OAT) (TOPCOAT) – that should keep you warm in winter (TOPCOAT),
23 One hopes to get a lot (BIDDER) from offer (BID-) to the German (‘the’ German = -DER) (BIDDER),
25 Display of the military (bugle/drum military display = TATTOO) characters in 17 across (‘tat’ = TAT-) as well (-TOO)? (TATTOO),
27 It goes over everyone’s head (SKY) in South (S-) Kerry (-KY)? (SKY),
29 Extremes of earth-shattering philosophy from Husserl (extremes of ‘EArth-shattering philosophy from husseRL’ = EARL), a noble sort? (EARL),
30 Most of those in 27 down (most of ‘sweets’ = SWEET), of course (SWEET),
31 They get fired by a major supplier (ARMS) for concealing what’s in farm subsidies (concealing what’s in ‘fARM Subsidies’ = ARMS)
34 Old Roman leader (TRIBUNE) from The Church (from the church/apse = TRIBUNE),
35 Unkind (mean), short (n) (‘meaN’ without ‘n’ = MEA-) row (-TIER) (MEATIER) is more powerful (MEATIER),
36 A measure of whiskey (SHORT) in small (S-), informal shot glass (pony) served up (= reverse indicator) (pony = -YNOP-) for relative (-SIS) (SHORT SYNOPSIS) that’s a little rundown (SHORT SYNOPSIS).
Down:
2 Frequent visitor (HABITUE) sounds surprised (HA-) at Institute (Institute of Technology = -IT-) and University (-U-) in Belgium (BE = -B-E) (HABITUE),
3 It’s apparent in uploaded (= reverse indicator) photograph circulating (it’s apparent in ‘photograpH CIRculating’ = hcir = RICH) of those rolling in dough (RICH),
4 A (A-) sorry State (plight) with no leader (p) (‘plight’ without ‘p’ = -LIGHT) (ALIGHT) in flames (ALIGHT),
5 In a corner (trapped) failing to get parking (p) (‘trapped’ without ‘p’ = traped)? Reverse (= reverse indicator) (traped = DEPART) and go someone else! (DEPART),
6 Finish filming (WRAP) of what’s on the menu in The Restaurant (WRAP)
7 Noble (EXALTED) and casual (lax = XAL-) swallowed up in Alien (ET = E-T-) with energy (-E-) from top down (top ‘Down’ = -D) (EXALTED),
8 Respiratory problem (SHORT OF BREATH) and so forth (so forth) playing (= anagram indicator) (so forth = SHORT OF) with slight wind (BREATH of wind) (SHORT OF BREATH),
9 Unable to pay for (SHORT) endless (t) fish (‘trouT’ without ‘t’ = TROU-) on boat (SS = -S-S) around Eritrea (-ER-) (SHORT TROUSERS) – presumably, it’ll form part of a suit in Bermuda (Bermuda SHORT TROUSERS),
14 Chinese way (Tao) of serving up (= reverse indicator) (Tao = OAT-) dessert (-CAKE) (OATCAKE) biscuit (OATCAKE),
16 Moderate (soften) loses the head (s) (‘Soften’ without ‘s’ = OFTEN) frequently? (OFTEN),
18 Some concern at a lough (some concerN AT A Lough = NATAL) in the old province overseas (NATAL is an old province of South Africa now called KwaZulu-Natal),
20 Not against (FOR) characters getting a rise (‘a rise’ = ‘arise’ = reverse indicator) in War Office (characters in ‘waR OFfice’ = rof = FOR),
21 The odd beauty (the odd letters of ‘BeAuTy’ = BAT) from club (BAT),
24 Drives (drives) out (= anagram indicator) (drives = DERVIS-) to Howth Head (‘Howth’ Head = -H) (DERVISH) with a member of religious order (DERVISH),
26 Name (term = TERM-) on island (-I-) for Ulster (-NI) (TERMINI) bus stations (TERMINI),
27 Candy (SWEETS) Snider leaves the dessert wines (‘snider’ leaves the ‘dessert wines’ = setwes = SWEETS),
28 First to yell (first to ‘Yell’ = Y-) out (= anagram indicator) names (names = -ES-MAN) (YES-MAN) to stooge (YES-MAN),
32 The response of the fat cat perhaps (PURR) to jeer from perjurer (to ‘jeer’ from ‘perjurer’ = prur = PURR),
33 Shocked reaction (GASP) up (= reverse indicator) in The Alps again (in ‘the alPS AGain’ - psag = GASP).