Across:
1 Just (RIGHT-) trying to remember (-THINKING) (RIGHT-THINKING) how a Conservative’s mind works (RIGHT-THINKING),
10 Local digs (local ‘digs’ = INSULTS) up all (= reverse all indicator) heads of small tender lettuces (heads of ‘Small Tender Lettuces’ = stl = -LTS) from America (US = -SU-) – the North (NI = IN-) (INSULTS),
11 Broadcast (-AIR-) flower (flower/river -OB-) in Ulster (N-I) (NAIROBI) from the green city in the sun (NAIROBI known as “The Green City in the Sun”),
12 Pick up on (HEAR) charm coming from March Hare (‘charm’ coming from ‘march hare’ = hare = HEAR),
13 Record (Extended Play record = -EP-) by tenor (-T-) in high definition (HD) reviewed (= reverse indicator) (HD = D-H) (DEPTH) in its complexity? (DEPTH),
15 Drop the sides of 23 across (drop the sides of ‘apathy’ = without ‘a’ + ‘y’ = PATH), of course! (PATH),
17 Sounds like (= homophone indicator) bun fight (‘row’ = ‘ROE’) with eggs (ROE),
19 Where in Monaco (Monaco/French ‘where’ = OU-), race (Tourist Trophy = -T-T) consumes Formula One (Formula One = -FI-) (OUTFIT) team (OUTFIT),
21 A (A-) leading entertainer (leading ‘Entertainer’ = -E-) in The Wild Bunch (mob = -MO-B-) is a (-A) (AMOEBA) parasite (AMOEBA)
22 Primate (GORILLA) produces revolutionary (guerrilla) report (= homophone indicator) (‘guerrilla’ = ‘GORILLA’),
23 Lack of interest (APATHY) in a (A-) track (-PATH-) by Yes (-Y) (APATHY),
25 One (-I-) foreign politician (-MP-) in Cork (lid = L-ID) (LIMPID) is crystal clear (LIMPID),
27 Mistake to drop item (‘mistake’ to drop ‘item’ = sak = ASK) from petition (ASK),
29 Confine (CAGE) to borders of Californian sage (borders of ‘CAlifornian saGE’ = CAGE),
30 Copper (CU-) can (tin = -T-IN) (CUT IN) switch lanes on the road dangerously (CUT IN),
31 Mark (exam mark = FAIR) and Cliona from California (‘Cliona’ from ‘California’ = afri = FAIR),
34 Minor argument (SPAT-) at university (University of Limerick = -UL-) linked to leading academic (leading ‘Academic’ = -A) (SPATULA) employed in the kitchen (SPATULA),
35 The whole story (the LOW-DOWN) of one depression after another (low + down = LOW-DOWN),
36 Entitlement (RIGHT) to open report (open ‘Report’ = R-) at any point (EVER-) to finish (-END) (RIGHT REVEREND) the minister’s address (RIGHT REVEREND).
Down:
2 Play (= anagram indicator) ain’t (aint = I-ANT) about national school (-NS-) with the lead (‘The’ lead = -T-) (INSTANT) from Brief Encounter? (INSTANT),
3 Room for hire (HALL) in hotel (H-) and in 21 down (‘all’ = -ALL) (HALL),
4 It’s a sample (TESTER) from street (street) cook (= anagram indicator) (street = TESTER),
5 Fire (IGNITE) iron initially (‘Iron’ initially = -I-) from back kitchen (back ‘kitcheN’ = -N-) in nice holiday cottage (Nice/French ‘holiday cottage’ = gite = -G-ITE) (IGNITE),
6 Cocktail (‘cocK’ tail = K-) from can (tin) knocked back (= reverse indicator) (tin = -NIT) (KNIT) by Bond (bond/join = KNIT),
7 One of the deliveries (NEONATE) is eaten on (eaten on) break (= anagram indicator) (eaten on = NEONATE),
8 The data protection commissioner will give you this (RIGHT OF ACCESS), I agree? (I agree = righto = RIGHT O-) With key (music key = -F) admission! (ACCESS) (RIGHT OF ACCESS),
9 Write (write) report (= homophone indicator) (‘write’ = ‘RIGHT’) on plot (land) without an intro (l) (‘land’ without ‘l’ = AND) and misrepresent (WRONG) (RIGHT AND WRONG) morality in its totality (RIGHT AND WRONG),
14 The smallest space (POKIEST) for pikes to (pikes to) swim (= anagram indicator) (pikes to = POKIEST),
16 Fit (RIGHT) for all sides today (RIGHT on all sides of today’s grid),
18 Sample of revolutionary (= reversal indicator), unparliamentary (‘unparLIAMEntary’ = liame = EMAIL) online exchanges (EMAIL),
20 Sinatra is out of stationary (‘sinatra’ is out of ‘stationary’ = TOY) – presumably, he’ll get it from dancer’s boss? (TOY from Dancer’s boss Santa),
21 Taken in by national leader? (taken in by ‘nationAL Leader’ = ALL) One hundred per cent! (ALL),
24 A (A-) party (Fine Gael = -FG-) to most of (y) the fodder (‘hay’ without ‘y’ = -HA-) coming back (= reverse indicator) in (in = -NI) (AFGHANI) from Kabul (AFGHANI),
26 Philosopher (PLATO-) is on (-ON) (PLATOON) something in company (PLATOON),
27 Leaders of an unusual political alliance, in reality (leaders of ‘An Unusual Political Alliance, In Reality’ = AU PAIR), a proponent of the nanny state perhaps (AU PAIR),
28 A month in Israel (KISLEV) or weekend (‘weeK’ end = K-) with Elvis (Elvis = -ISLEV) all over the place (= anagram indicator) (KISLEV),
32 Shogun’s missing son (‘shoguns’ missing ‘son’ = hgus = GUSH) is Flood? (flood = GUSH),
33 Drain (sewer) head off (s) (sewer’ without ‘s’ = EWER) jug of beer perhaps (EWER).