Across:
1 Where people tend to lose their seat by the sounds of it? (MUSICAL CHAIRS) That would be party games! (MUSICAL CHAIRS),
10 The most grotesque (UGLIEST) middle-age (middle ‘age’ = -G-) fiction (-LIE-) and extreme stories (extreme ‘stories’ = -S-) in Utah (U-T) (UGLIEST),
11 Serving (PLATE-) a (-A-) university (-U) (PLATEAU) that’s plainly on the rise (PLATEAU),
12 Longing (ITCH) to head off (p) to the ground (‘pitch’ without ‘p’ = ITCH),
13 The Blues (MUSIC) component on all sides today (MUSIC on all sides of today’s grid),
15 Wiki (Wiki = KIWI) misprint? (= anagram indicator) That’s not likely to fly! (KIWI),
17 It’s upside down (= reversal indicator) in Brunei pirate (in ‘Brunei pirate’ = eip = PIE) chart (PIE),
19 Fight (bout = B-OUT) over dude (guy) losing the head (g) (‘guy’ without ‘g’ = -UY-) (BUYOUT) with action taken by company involved in procurement (BUYOUT),
21 Miss (miss = M-SSI-) out (= anagram indicator) over a (-A-) frequency (-F) (MASSIF) or range (MASSIF),
22 Take the science out of encyclopaedias (taking the ‘science’ out of ‘encyclopaedias’ = ylopada = PAYLOAD) and use it to fill the rocket (PAYLOAD),
23 Cures (cures = SUC-ER) model (= anagram indicator) consuming potassium (-K-) (SUCKER) in dope (SUCKER),
25 Flowery types of Rosé (flowery types of rose = PETALS) and Port (P-) knocked back (= reversal indicator) on the tab (on the slate = -ETALS) (PETALS),
27 Belonging to estate agent (belonging to ‘estate agent’ = TEA) of Earl Grey (TEA),
29 Orderly (NEAT) produces sample of medicine attentively (sample of ‘medicine attentively’ = NEAT),
30 Olympic symbol (TORCH) held by Francie Barrett or cheerleader (held by ‘Francie Barrett or cheerleader’ = TORCH),
31 Food store specialist (DELI) in Dandelion Market (in Dandelion Market = DELI),
34 Dishes (dishes = S-EDISH) rubbish (= anagram indicator) about women (-W-) (SWEDISH), in a manner of speaking (SWEDISH),
35 Built (= anagram indicator) Nazi car (Nazi car = CZARINA) for one of the Russian leaders (CZARINA),
36 Classy types instrumental (MUSIC TEACHERS) in showcasing the differences between Bass and Harp (MUSIC TEACHERS).
Down:
2 A French (a = UN-) woman (Lucy = -LUC-Y) over the weekend (‘week’ end = -K-) (UNLUCKY) is not charmed (UNLUCKY),
3 The concept (IDEA) of some outside agency (some ‘outside agency’ = IDEA),
4 Carries on (carries on/misbehaves = ACTS UP) with plays (ACTS) and leads under pressure (leads ‘under pressure’ = UP) (ACTS UP),
5 Part of the competition (CUP TIE) caught (C-) up (-UP) with Bond (bond/link = -TIE) (CUP TIE),
6 Alsatian ain’t leaving (‘Alsatian’ ain’t leaving/ without ‘aint’ = lsaa = ALAS) unfortunately (ALAS),
7 Prepares another draft (RE-EDITS) for one (-I-) in desert (desert = RE-ED-TS) production (= anagram indicator) (RE-EDITS),
8 What goes into the score (MUSIC) and dealing (BUSINESS) (MUSIC BUSINESS) is collectively responsible for giving person of note a record (MUSIC BUSINESS),
9 Killed (‘slain’ = ‘Slane’ MUSIC FESTIVAL) broadcast (= homophone indicator) from Woodstock (MUSIC FESTIVAL),
14 It’s more ludicrous (SILLIER) in retrospect (= reversal indicator) – Ellis (Ellis = SILL-E-) Island (-I-) is guarded by regiment (-R) (SILLIER),
16 French street (French ‘street’ = RU-E) contains gym (-PE-) (RUPEE) – the Indians get their money’s worth out of it (RUPEE),
18 Looks washed out (FADED) in French capital (‘French’ capital = F-) with dead (dead = -ADED) heat (= anagram indicator) (FADED),
20 The Amazon River heads (‘the Amazon River’ heads = TAR) out on The Atlantic Ocean, for example (old sailor = TAR),
21 Politician (M-P) taking in America (-A) (MAP) would be lost without this (MAP),
24 Could start (‘could’ start = C-) to loathe (-HATE-) a (-A-) classy (upper class = -U) (CHATEAU) nice source of wine (Nice/French wine from CHATEAU),
26 Swallowed (ATE-) deception (-LIE-) at republican (-R) (ATELIER) workshop (ATELIER),
27 Path to (path to = TOP HAT) complex (= anagram indicator) is by the milliner’s presumably (TOP HAT is by/created by the milliners),
28 Account (AC-) by a (-A-) group of spies (-CIA) (ACACIA) – one is a plant (ACACIA),
32 One of the player’s (HI-FI player) characters in Delhi fiction (characters in “Delhi fiction” = HI-FI),
33 Hit (LASH) by streams coming out of salt marshes (‘streams’ coming out of ‘salt marshes’ = lash = LASH).