Across:
1 Verve (pep) lose the head (p) (“pep” without “p” = -EP-) in dive (dive = dart = D-ART) (DEPART) in Split (split = DEPART),
4 Charming (ADORABLE) American (A-) puts up (= reversal indicator) Corsican neighbour (Elba = -ABLE) from bar (bar/rod = -DOR-) (ADORABLE),
9 Making fun of (PARODY) staff (staff/stick = -ROD-) consumed by wages (PA-Y) (PARODY),
10 Fool (ASS-) around (-O-) with broadcaster (-RTE-) and department (-D) (ASSORTED) of various types (ASSORTED),
12 A loud (aloud = homophone indicator) relative (“son” = “sun” = SUN-) is depressed (-DOWN-) in hospital (-ER) (SUNDOWNER) with the drink of late (SUNDOWNER),
13 Insolvency (RU-IN) over direction (direction north = -N-) (RUN-IN) leads to quarrel (RUN-IN),
14 Car (model T-) competition (-RACE) with component (ELEMENT) (TRACE ELEMENT) promoted on the box for foodie types (TRACE ELEMENT),
18 Bypass (OUTMANOEUVRE) revealed (OUT-) by engineer (-MANOEUVRE) (OUTMANOEUVRE),
21 No gins in Singapore (no “gins” in “Singapore” = apore = OPERA) for the drinking song presumably in La Traviata (“Let’s drink from the joyful cups” from Verdi’s La Traviata = OPERA),
22 Doctor (= anagram indicator) ain’t (aint = ANTI-) getting infection (-VIRUS) (ANTIVIRUS) from destroying worms? (ANTIVIRUS destroying computer worms),
24 Fabulous type (TERRIFIC) from Dandy? (TERRIFIC),
25 A set routine (in a GROOVE) to order (-O-) in a group of trees (grove = GRO-VE) (GROOVE),
26 Stick (CL-ING) around college official (dean) losing the head (d) (“dean” without “d” = -EAN-) (CLEANING) working with the Polish (working with the polish = CLEANING),
27 IT Dept (IT Dept = PITTED) fixed (= anagram indicator) what happened to the dates (PITTED).
Down:
1 Part payments for (DEPOSITS) butcher’s (= anagram indicator) topsides (topsides = DEPOSITS),
2 Secretary (PA-) gets temporary lease (-RENTAL) (PARENTAL) of life – support you’d associate from The Elders (PARENTAL),
3 A Dior (a Dior = RADIO) dress (= anagram indicator) for one of the mediums? (RADIO),
5 Only over 21s allowed (DISCRIMINATE) to tell the difference (DISCRIMINATE),
6 Ordering a (ordering a = RIO GRANDE) structure (= anagram indicator) divides the Americans and Mexicans (RIO GRANDE),
7 Snapping at (BITING) segment (BIT-) in (-IN-) Government (-G) (BITING),
8 Awaiting decision (pending) with no introduction (p) (“pending” without “p” = ENDING) or conclusion (ENDING),
11 A hot, painful reaction (INFLAMMATION) to a (-A-) couple of Frenchmen (Messieurs x 2 = M+M = -MM-) consumed by rising costs (inflation = INFL-ATION) (INFLAMMATION),
15 Cautioned (cautioned = EDUCATION) playing (= anagram indicator) in the classy practice for those in the academy (EDUCATION),
16 Wrapped up (OVER-) by firm (-CO-) with a (-A-) time (-T) (OVERCOAT) in the colourful shop perhaps (OVERCOAT paint),
17 Those in the hotel (BEDS-) having drink (-TEA-) with director (-D) (BEDSTEAD) supporting that lot out for the night (BEDSTEAD),
19 The essence of Easter 1916 (the essence of Yeats’ poem Easter 1916 = POETIC), for one, provides a type of justice (POETIC justice),
20 Piece of countryside greenbelt (piece of “countryside greenbelt” = DEGREE) comes with a qualification (DEGREE),
23 Composed notes in Italian for 21 across (VERDI composed “opera”) to drive (drive = VERDI) engineer (= anagram indicator).