Across:
8 Make a difference (MATTER) to the runner (MAT-) starting treatment (starting ‘Treatment’ = -T-) in hospital (-ER) (MATTER),
9 Old boat (ark) returning (= reverse indicator) (ark = KRA-) with first officer (first ‘Officer’ = -O-) consumed by martial arts workout (kata = -KAT-A) (KRAKATOA) from Indonesian volcanic island (KRAKATOA),
10 Composed (CALM) segment of physical map (segment of ‘physiCAL Map’ = CALM),
11 Americans would consider this gas (PETROL) on a bike (PUMP) (PETROL PUMP), as anyone with electric wheels locally (‘wheels’ locally = car) would be looking for an alternative! (PETROL PUMP),
12 American party (Grand Old Party = G-OP) taking in area (-A-) on the outskirts of Listowel (the outskirts of ‘Listowel’ = -LL-) (GALLOP) for the horse’s run on the racecourse (GALLOP),
14 Positions (OPINIONS) of duck (O-) wings? (-PINIONS) (OPINIONS),
15 Old French (Old French = OF) behind (= position indicator) 8 across (‘matter’ = MATTER) and most of those in 14 across? (most of ‘opinions’ = OPINION) (MATTER OF OPINION) That’s open to debate! (MATTER OF OPINION),
18 Official permission (APPROVAL) for a (A-) park (-V-) sign (-V- sign) in polar (polar) wild (= anagram indicator) (polar = -PRO-AL) (APPROVAL),
20 Mark’s successor (EURO- successor to German mark) gets capital punishment (capital ‘Punishment’ = -P-) for extreme crime (extreme ‘crimE’ = -E) (EUROPE) in our community (EUROPE),
22 To help out (CONTRIBUTE) criminal (CON-) with expression of praise in statement (-TRIBUTE) (CONTRIBUTE),
24 Little (SIZE) and Large? (SIZE),
25 Find and bring back (RETRIEVE) by meandering (= anagram indicator) River Tee? (river tee = RETRIEVE),
26 Supporter on The Hill (Dub = D-UB-) consumes duck (-O-) with the foreign (‘the’ foreign/French = -LE) (DOUBLE) drink, a large one (DOUBLE).
Down:
1 Unmanageable without legume (‘unmanageable’ without ‘legume’ = nanaab = BANANA) or fruit (BANANA),
2 Check (STEM) both sides of Stewart’s Theorem (both sides of ‘STewart’s theorEM’ = STEM),
3 Material for a drawer in a school (ART PAPER) – the type anyone doing a rough sketch could draw on? (ART PAPER),
4 Weekend (‘weeK’ end = -K-) in South African (SA = S-A-) and time (-T-) (SKAT) for a game (SKAT),
5 One (-I) taking shifts in the factory (rotas) arising (= reverse all indicator) (rotas = SATOR-) (SATORI) out of what the Buddhists say is enlightening (SATORI),
6 Grecian map (Grecian map) adapted (= anagram indicator) (Grecian map = CAMPAIGNER) by one of The Crusaders (CAMPAIGNER),
7 College (C-) at the end of term (end of ‘terM’ = -M-) in Arabian country (Oman = -OM-AN-) has party (-DO) (COMMANDO) for one going on The Missions (COMMANDO),
13 Left (L-) to rehearse (repeat/iterate = -ITERAT-E) around old city (-UR) with Dubliners (James Joyce’s Dubliners) (LITERATURE) and other bookish types (LITERATURE),
14 County (Offaly) is short (y) (‘Offaly’ without ‘y’ = OFFAL) of waste material (OFFAL),
16 Supported (APPROVED) Dubs from the start (‘Dubs’ from the start = -D) after (= position indicator) sanction (APPROVE-) (APPROVED),
17 Puts on an act (PRETENDS) with unpredictable (= anagram indicator) serpent (serpent = PRETEN-S) around Land’s End (land’s ‘enD’ = -D-) (PRETENDS),
19 States (states = VOICES) where there’s nothing (-O-) in crime and corruption (V-ICES) (VOICES),
21 This is one (PUZZLE) tough conundrum, for instance (PUZZLE),
23 Bruised, missing rib (‘bruised’ missing ‘rib’ = used = USED) and worn out (USED),
24 Record (record potato = SPUD) for setting up (= reverse indicator) duty free shops in a roundabout way (‘DUty free shoPS’ in a roundabout way = dups = SPUD).