Across:
1 Stick (bat = TAB-) up (= reversal indicator) for the French (the = -LE-) school (-S) (TABLES) used by the mathematicians (TABLES),
4 Disturbed (SHAKEN UP) by sheik (‘sheik’ = ‘shake’ = SHAKE-) on the radio (= homophone indicator) – a bit of a wit (pun = -N UP) in retrospect (= reversal indicator) (SHAKEN UP),
9 Confederates (ALLIES) of gangster (AL- Capone) generally arrive in a pack (‘pack of lies’ = -LIES) (ALLIES),
10 Sign (CLUE-) for takeaway (take away = -LESS) (CLUELESS) completely in the dark (CLUELESS),
12 That violent shower (HAILSTORM) in this moral (this moral = HAILSTORM) maze (= anagram indicator),
13 Paper (Financial Times = F-T) covers swimmer (eel) retiring (= reversal indicator) (eel = -LEE-) (FLEET) and going overseas to meet rivals (FLEET),
14 Does this mean miserable type (PENNY-PINCHER) has their hand in the English till? (PENNY-PINCHER),
18 To be overly enthusiastic with one of the pieces (be TRIGGER-HAPPY with one of the pieces/pistol) could set off (TRIGGER-) one of the Seven Dwarfs (-HAPPY) (TRIGGER-HAPPY),
21 Takes out (OMITS) Anne from Minnesota (‘Anne’ from ‘Minnesota’ = OMITS),
22 Take another look (RE-EXAMINE) about (RE-) for note (music note -E-) to Maxine (Maxine = -XAMINE) Rock (= anagram indicator) (RE-EXAMINE),
24 Review (CRITIQUE) of Rising? (= reversal indicator) Irish (I-) Republican (-R-) Council (C-) = quite (quite = -TIQUE) upset! (= anagram indicator) (CRITIQUE),
25 Party (DO-) slump (-SAG-) relates to extreme indiscipline (extreme ‘indiscipline’ = -E) (DOSAGE) – this might come precisely as a shot in the arm (DOSAGE),
26 Bar (BLOCKADE) musical type (rock) losing the head (r) (‘rock’ without ‘r’ = -OCK-) consumed by a bit of grass (blade = BL-ADE of grass) (BLOCKADE),
27 Scores an equaliser (LEVELS) in line (LEVEL-) with last defenders (last ‘defenders’ = -S) (LEVELS).
Down:
1 Dances (-HOPS) after (= positional indicator) drinks (TEAS-) (TEASHOPS) in room for refreshments (TEASHOPS),
2 Invoice (BILL-) is charged (-ION-) to Society (-S) (BILLIONS) keeping all the banks afloat presumably (BILLIONS),
3 What’s the chances (EVENS) of veterans getting rid of rat? (‘veterans’ getting rid of ‘rat’ = veens = EVENS),
5 Sounds excited (HOLY MACKEREL) by description of angelfish perhaps (HOLY MACKEREL),
6 Chill (KEEP FRESH) in brand new (FRESH) castle (KEEP) from the start (= position indicator) (KEEP FRESH),
7 Caught (-C-) in Seine (Seine = NIE-ES) swimming (= anagram indicator) (NIECES) with female members of family (NIECES),
8 Appreciates missing Capri (‘appreciates’ missing ‘Capri’ = apetes = PESETA) – an old European capital (old capital/money = PESETA),
11 Failing to take advantage of (LOSING) initially generous (initially ‘generous’ = G-) bar order (-ROUND) (LOSING GROUND), as not keeping up with others (LOSING GROUND),
15 Standard (YARDSTICK) of Tracy’s kid (Tracy’s kid = YARDSTICK) running (= anagram indicator),
16 Goes off (SPOILAGE) with head barman (Attorney General = -AG-) on treat (SPOIL-) to Spain (-E) (SPOILAGE),
17 Ceremonial fire (PYRE-) seen (seen = -NEES) changing direction (= reversal indicator) (PYRENEES) from a height in France (PYRENEES),
19 The young of a sly type (FOX CUB) from Ring (-O-) gets cross (-X) with copper (CU-) consumed by Facebook (F-B) (FOX CUB),
20 First-class (AI-) miner (‘miner’ = ‘minor’ = -KID-) says (= homophone indicator) nothing (-O) (AIKIDO) as a form of self-defence (AIKIDO),
23 Love (ADORE) what’s found in bread? Oregano! (what’s found in ‘bread oregano’ = ad ore = ADORE).