Across:
1 Lost for words (AMAZED) in an open ('An' open = A-), old prison (-MAZE-) for five hundred (Roman 500 = -D) (AMAZED),
4 Theologian (-DD-) taken in by Evita (Evita) all over (= reverse indicator) (Evita = A-TIVE) (ADDITIVE) The Supplement? (ADDITIVE),
9 Open letter dismisses plot (‘open letter’ dismisses ‘plot’ = eneter = ENTRÉE) – of course, it gets the juices flowing (ENTRÉE).
10 Rome reps (more reps) travelling (= anagram indicator) (more reps = EMPERORS) for those expanding into new territories (EMPERORS),
12 Sweeping (BROAD) existing (being) report (= homophone indicator) (‘being’ = ‘BEAN) (BROAD BEAN) produced by Pulse (pulse = BROAD BEAN),
13 Retweet (RT = R-T) about starters of Asian snacks (starters/first letters ‘Of Asian Snacks’ = -OAS-) (ROAST) for Sunday lunch (ROAST),
14 Captured (taken = TAKE N-) by old (-O) spy (NOTICE) (TAKE NO NOTICE) in bypass (TAKE NO NOTICE),
18 Post worker (worker at ‘The Post’ = NEWSPAPERMAN) runs daily (NEWSPAPERMAN),
21 Measured drinks (UNITS) in the army mess presumably (UNITS),
22 Allotment (ALLOWANCE) permit (ALLOW-) for area (-A-) near back garden (back/rear ‘gardeN’ = -N-) and church (Church of England = -CE) (ALLOWANCE),
24 State (KENTUCKY) of English county (KENT-) – fortuitous (lucky) without a leader (l) (‘lucky’ without ‘l’ = -UCKY) (KENTUCKY),
25 Employed in a studio (ARTIST), in part, I stress (in ‘pART I STress’ = ARTIST)
26 Chew the cud (chew the cud/contemplate = MEDITATE) as friend (mate = M-ATE) consumes mixed (= anagram indicator) diet (diet = -EDIT-) (MEDITATE),
27 Tub from start (“Woman in a Tub” from start = -T-) in Degas (Degas) retrospective (= reversal indicator) (Degas = S-AGED) (STAGED) is not natural (STAGED).
Down:
1 A (A-) European (Serb) loses the head (s) ('Serb' without 's' = -ERB-) in Paris, for instance (city = -C-ITY) (ACERBITY), out of bitterness, in a manner of speaking (ACERBITY),
2 Earn a living (-WORK-) investing in rock (= anagram indicator) star (star = ART-S) (ARTWORKS) in the pictures (ARTWORKS),
3 Polish (polish/revise = EMEND) characters taken in by The Wise Men deceived (characters taken in by ‘the wisE MEN Deceived’ = EMEND) by Polish,
5 It’s beyond doubt (DEMONSTRABLE) brute (DEMON-) gets head right (head ‘Right’ = -R-) in Arabian accommodation (Arabian/horse accommodation = -ST-ABLE) (DEMONSTRABLE),
6 One (I-) buck (deer = -DEE R-) at closing time (closing ‘timE’ = -E-) gets stick in snooker hall (-ÇUE) (IDÉE REÇUE) – it’s a notion the French generally accept? (IDÉE REÇUE),
7 Front line (ISOBAR) summits of Sabalan, Oshtorankuh, Bazman, Alam-Kuh (summits of ‘Sabalan, Oshtorankuh, Bazman, Alam-Kuh’ = -SOBA-) in Iran (IR = I-R) (ISOBAR),
8 Stargazer loses rag (‘stargazer’ loses ‘rag’ = stazer = ERSATZ), as it’s not as good as the real thing (not real/genuine = ERSATZ),
11 Time (T-) in 20 down (sinned) winding-up (= reverse indicator) most of those (d) (‘sinned’ without ‘d’ = sinne = -ENNIS) linked to shady business (RACKET) (TENNIS RACKET) in the hands of court entertainer (TENNIS RACKET),
15 Can’t live without (NEEDS) grape juice (MUST) (NEEDS MUST) and it’s unavoidable (NEEDS MUST),
16 Correcting (EMENDING) engineer (E-) putting things right (-MENDING) (EMENDING),
17 Student (student) travelling (= anagram indicator) (student = UNT-STED) around Spain (-E-) (UNTESTED) didn’t go for trials (UNTESTED),
19 It doesn’t make sense (BUNKUM) this is somewhere to put one’s head down (BUNK-) ahead of university (ahead of ‘University’ = -U-) final exam (final ‘exaM’ = -M) (BUNKUM),
20 Acted badly (SINNED) around (= reverse indicator) part of Clare (Ennis = SINNE-) and Dublin (-D) (SINNED),
23 The most unpleasant (WORST), upsetting (= reverse indicator) row (row = WOR-) with Saint (-ST) (WORST).