Across:
1 Finishes 14 across (finishes ‘family circle’ = CIRCLE) in ring (ring = CIRCLE),
4 Too much confidence in one’s own depiction (EGOMANIA) in image on a (image on a) building (= anagram indicator) (image on a = EGOMANIA),
9 Carry the can without Harry (‘carry the can’ without ‘Harry’ = catecn = ACCENT) or Mark – that’s a stress speaking French (mark that’s a stress speaking French = ACCENT),
10 Starters of eggs cooked (starters of ‘Eggs Cooked’ = -EC-) on weekend (‘weeK’ end = -K-) in Holland (NL = N-L-) at first-class (-ACE) (NECKLACE) chain (chain = NECKLACE),
12 Reviews (= reverse indicator) Friends (friends/pals = SLAP-) for The Post (post/stick = -STICK) (SLAPSTICK) as it’s a farce (SLAPSTICK),
13 Give out (ALLOT) to Rod coming off toll road (‘Rod’ coming off ‘toll road’ = tolla = ALLOT),
14 Group of relatives (FAMILY CIRCLE) in the house (FAMILY) band (CIRCLE) (FAMILY CIRCLE),
18 Modern (NEW) Greenland (Greenland) confused (= anagram indicator) (Greenland = ENGLANDER) (NEW ENGLANDER) by a citizen of America from the east coast (NEW ENGLANDER),
21 The illicit affair (AMOUR) of removing pests from mousetraps (removing ‘pests’ from ‘mousetraps’ = moura = AMOUR),
22 Put out (INDIGNANT) by colourful type (indigo), for the most part (o) (‘indigo’ without ‘o’ = INDIG-), sending up (= reverse indicator) article (an = NA-) and good books (Old Testament = -NT) (INDIGNANT),
24 Strike (RAP) songs (MUSIC) (RAP MUSIC) synonymous with the beat on the street (RAP MUSIC),
25 On edge (rim = R-IM-) covering up, for example (e.g. = -EG-), engineering (-E) (REGIME) group in administration (REGIME),
26 A typical example of (PARADIGM) folding over (= reverse indicator) map (map = PA-M) covering summit on Greek (summit on ‘Greek’ = -G-) mountain on Crete (Mount Ida = Ida = -ADI-) at side of the road (at side of ‘road’ = -R-) (PARADIGM),
27 Cuts corners (SKIMPS) to quickly read (SKIM-) front page (front ‘Page’ = -P-) and sports on the back (‘sportS’ on the back = -S) (SKIMPS).
Down:
1 Put in sets of (CLASSIFY) wild (= anagram indicator) salsify (salsify = -LASSIFY) behind (= position indicator) head of cabbage (head of ‘Cabbage’ = C-) (CLASSIFY),
2 Asks for rebate again from Revenue (RECLAIMS) offering to work (= anagram indicator) miracles (miracles = RECLAIMS),
3 Bond’s (bonds/links = LINKS) relationship (LINK-) with the head of Spectre? (head of ‘Spectre’ = -S) (LINKS),
5 23 down (‘greek’ = GREEK) linked play that was moving (TRAGEDY) (GREEK TRAGEDY) for Ajax, the Sophoclean type (“Ajax” is a GREEK TRAGEDY by Sophocles),
6 Create (MAKE) place (PL-) with energy (-E-) surrounded by non-drinkers (AA = A -A) (MAKE A PLEA) from petition (MAKE A PLEA),
7 Hesitantly drops this (‘hesitantly’ drops ‘this’ = eantly = NEATLY) in an orderly fashion (NEATLY),
8 Gladstone ignored old (‘Gladstone’ ignored ‘old’ = gastne = AGENTS) spies (AGENTS),
11 Record (DISC-) for writing (from the 3Rs = -R-) and working on film (-EDITING) (DISCREDITING) is giving someone a bad name (DISCREDITING),
15 Relax (LIE AROUND) with a (A-) few drinks from the bar (-ROUND) after (= position indicator) a whopper (LIE) (LIE AROUND),
16 Papers (ID-) from Spain (-E-) linked to the greatest (-ALI-) manuscript (MS = -SM) reflecting (= reverse indicator) (IDEALISM) unrealistic pursuit of perfection (IDEALISM),
17 Time (T-) scoundrels (-ROTTERS) (TROTTERS) spread out keeping the swine on his toes (TROTTERS),
19 Sparta (Sparta = SATRAP) built (= anagram indicator) by old provincial governor (SATRAP),
20 See (see) you (you) shortly in conversation (= homophone indicator) (‘see’ = ‘c’ + you = ‘u’ = Cu = short for COPPER) with Penny? (penny = COPPER),
23 Presumably Plato expressed this (GREEK) or did I read that in his Apology? (Plato’s Apology written in GREEK).