Across:
1 Disregard advice to shut up (OPEN ONE’S MOUTH) and sing to the locals (to ‘sing’ locally means to OPEN ONE’S MOUTH),
10 Cast (PROJECT) from the arts centre (The PROJECT Arts Centre),
11 Posted (posted = DES-TOP) novel (= anagram indicator) over the weekend (‘week’ end = -K-) (DESKTOP) from computer (DESKTOP computer),
12 Not a pretty sight on top of everything (‘not a pretty sight’ on top of everything = NAPS) for the gamblers (NAPS),
13 Take exception (DEMUR), as natives aren’t part of misadventure (‘natives’ aren’t part of ‘misadventure’ = mdure = DEMUR),
15 Presently (ANON), a fragment of Ottoman ontology (a fragment of ‘Ottoman ontology’ = ANON),
17 Is involved in the arrangement (is involved in the ‘arrangement’ = GEM) for one of The Stones (GEM stones),
19 Rosemary (HERB-) gets first (-A-) pound (pound = £ = -L) (HERBAL) of tea (HERBAL tea),
21 Crude (OIL-) leader-column (leader ‘column’ = -C-) article (-AN) (OILCAN) fuels transport problem (OILCAN),
22 Reveal (reveal = LE -AVRE) drunk (= anagram indicator) consumes hot (H-) (LE HAVRE) port, which is big in France (LE HAVRE port),
23 Pussy foot (paw = WAP-) around (= reversal indicator) centre with (centre ‘with’ = -IT-) one (-I) (WAPITI) buck (WAPITI deer /stag),
25 Sultan is missing from the publication’s (‘Sultan’ is missing from the ‘publications’ = pbicid = BIOPIC) autobiographical film (BIOPIC),
27 In Berlin, the (‘German ‘the’ = der = RED) cutbacks (= reversal indicator), politically speaking, could undermine the capital? (RED / revolutionary wants to undermine the capital? / capitalism),
29 Newspaper columnist sides (‘newspaper columnist’ sides = NEST) with one of those uppity sorts – it’s for the birds (NEST),
30 Call for help (-SOS) after (= positional indicator) exercise (PE-) (PESOS) in South American capital (capital/money = PESOS),
31 Champion (HERO) one of those trapped in the rounds (one of those trapped ‘the rounds’ = HERO),
34 Give too much (OVERPAY) volume (-V-) in opera (opera = O-ERPA-) production (= anagram indicator) for last melody (last ‘melody’ = -Y) (OVERPAY),
35 Love (EMOTION) Hate? (EMOTION),
36 Is this what surgeon might do at centre (OPEN ONE’S HEART) to let it be known what’s going on inside? (OPEN ONE’S HEART).
Down:
2 Bloom (PROSPER) – one of Shakespeare’s unfinished characters? (Shakespeare’s ‘Prospero’ without ‘o’ = PROSPER),
3 Ne’er -do-well dismisses Orwell (‘neer do well’ dismisses ‘Orwell’ = need = NEED) as a basic requirement (NEED),
4 Odd (= anagram indicator) menu (menu = NU-ME-) includes tea (-T-) with little measure (gram = -G) (NUTMEG) of spice (NUTMEG),
5 Some (“some” = “sum” = S-UM) speech (= homophone indicator) covering what groom said (‘I do”) back (= reversal indicator) to priest (I do = -ODI-) (SODIUM) makes 16 down what it is (SODIUM is ‘salty’),
6 Remove from office (OUST) piece of spurious technology (piece of ‘spurious technology’ = OUST),
7 Attic in (attic in = TITANIC) building (= anagram indicator) is huge (TITANIC),
8 Produce draft (OPEN THE WINDOW) and give it a good airing in The House (OPEN THE WINDOW),
9 Frank (OPEN), and shortly (n) Ann (Ann) (‘Ann’ without ‘n’ = AN), gets Bill (ACCOUNT) (OPEN AN ACCOUNT) to start to save for a rainy day (OPEN AN ACCOUNT),
14 Intimidates (MENACES) with three jacks, for example (three Jacks = MEN-), and a couple of top cards (-ACES) (MENACES),
16 Describes briny solution (SALTY) of oil taken from loyalist (‘oil’ taken from ‘loyalist’ = lyast = SALTY),
18 Don’t get up (LIE-IN) from bar leaving Liberian (‘bar’ leaving ‘Liberian’ = liein = LIE-IN)
20 Blooming loop (garland of flowers = LEI) that’s part of the bobsleigh (that’s part of the ‘bobsleigh’ = LEI),
21 Spherical object (ORB) integral to conveyor belt (integral to ‘conveyor belt’ = ORB),
24 Arrange the decoration (PASTE-UP wallpaper) for old (PAST-) EU (-E U-) park (-P) (PASTE-UP),
26 Pierre (Pierre = PRE-IER) welcomes Frenchman (-M-) (PREMIER) as head of government (PREMIER),
27 Have confidence in (RELY ON) or about (RE-) French city (Lyon = -LY ON) (RELY ON),
28 Quite a few (DOZENS) zoned (zoned = DOZEN-) out (= anagram indicator) at school (-S) (DOZENS),
32 Ready for business (OPEN) with all sides today (OPEN on all sides of today’s grid),
33 Pay attention to (NOTE) bank’s nominal rate (banks ‘nominal rate’ = NOTE).