1 Girl returns with small hound (6)
HARASS Random girl is SARAH, reversed/returned with S(mall) tacked on the end
5 About a thousand in Italy involved in disaster (8)
CALAMITY About CA (circa) a thousand: M (just coincidence or distraction that it’s a thousand in Roman era Italy), the rest surrounding the M is an anagram (involved ) of ITALY
9 Republican invested in key American plant (8)
MARJORAM A plant in the category of “known because I cook with it”. Key translates to MAJOR, insert R(epublican) and tack AM(erican) on the end
10 Player such as Cowdrey getting six for a hundred (6)
VIOLIN Acceptable, I think, to have a musician defined by the instrument played. Younger solvers (and many not interested in cricket) may not know that Cowdrey’s first name was Michael, but he was known by his middle name COLIN. I remember him coming in to bat with his arm in plaster against the fearsome West Indies’ Wes Hall and Charlie Griffith to salvage a draw. I was privileged to see Hall and Griffiths playing for a Wanderers team in 1979 in, of all places, Totnes in Devon. Still pretty fearsome even then.
Back to the clue: take COLIN, replace the hundred C with six VI
11 Turning around, ruffian grabs publicity thing (6)
DOODAH Our ruffian is a HOOD, insert AD for publicity and reverse the whole thing
12 Publicise search for firearm (3,5)
AIR RIFLE A simple charade: publicise AIR, search RIFLE
14 Journalist loses right to identify alleged adulterer (2-10)
CO-RESPONDENT Your journo is a CORRESPONDENT who is negligent of one of his R(ight)s. Chambers can’t be bothered with the hyphen, but I think it’s better with. Back in the day, you’d divorce your spouse for adultery, and the suspected third party would be the co-respondent with some rather natty two-tone shoes to emphasise (in this case) his caddishness.
17 Another refitted ship's back from Tyneside? (12)
NORTHEASTERN An anagram of ANOTHER turns out to be NORTHEA, to the back of which you fit the back of a ship. Um, STERN
20 Charming island with bar area that's set back (8)
ADORABLE Bar area? Snug? Lounge? Nope. The random island is ELBA, the bar is a ROD and Area provides the A. Reverse all.
22 Surgeon firstly uncovered wound (6)
SNAKED Surgeon first is, of course S. Add NAKED for uncovered. Not that sort of wound
23 Airline once located centrally in country (6)
PANAMA According to 2001, Pan Am was operating the shuttle form Earth to the great wheeling space station. It didn’t last that long, collapsing in 1991, but in much of its lifetime seemed invincible, too big to fail. Anyway, take it, add the middle of located (centrally) which turns out to be A, and voila!
25 Having high output for short duration — one critic's conclusion (8)
PROLIFIC For: PRO, short duration LIF(e), one; I, critic’s conclusion: C
26 Put firearm in corner, perhaps (3,5)
SET PIECE Now that footie is back, albeit with those eerie recorded not-there crowds, the setter can be forgiven for the reference. Set pieces are corners, free kicks and other such advantages to the attacking side. Put: SET, firearm: PIECE
27 Vessel's new keel regularly maintained by sailor (6)
TANKER New just contributes its N, KeEl its alternate letters (“regularly”) and the sailor “maintaining” them is a TAR
2 A newspaper operating in part of Spain (6)
ARAGON A newspaper is A RAG, operating is ON. Now you know where Henry got Catherine from
3 One settling dispute in middle of road? Just schedule some coppers to turn up (11)
ADJUDICATOR A rare example of the “middle of” clue spreading over two words, in this case roAD JUst. Then schedule is ROTA, and some coppers CID, joined and reversed (to turn up)
4 Extra tax daily covered by sharp increase (9)
SURCHARGE Daily is the woman who does, the CHAR, in this instance surrounded by SURGE for sharp increase, as currently seen in some American states struggling with Covid 19. Stay safe!
5 Constant revision of maps in cartographer's range (7)
COMPASS Constant is C, “revision” of MAPS gives you MPAS, contained in OS, the Ordnance Survey map-making brand
6 Left state in old vessel (5)
LAVER Now mostly an ecclesiastical basin, I think. Simple enough: L(eft) plus AVER for state
7 Briefly feeling low (3)
MOO MOOD cut short.
8 Two cracks, one said to be insignificant (8)
TRIFLING Only just got this. The two cracks are TRY and FLING, but the first one is said, giving TRI
13 Tend to get upset in current state: depression (11)
INDENTATION An anagram (upset) of TEND in current: I and state: NATION
15 Go too far having completed project (9)
OVERSHOOT One of several possibilities, given the range of synonyms for project. I started with REACH (not as good, but not impossible). Completed provides OVER
16 Hefty type of cable split across diameter (4,4)
BOLD FACE (QED) an anagram (split) of OF CABLE “across” Diameter. Wasted a lot of time looking for a type of cable and a word meaning hefty derived from it
18 Metal point absorbs pressure in tall structure (7)
STEEPLE The metal is STEEL, the point E (from a set of four) and P(ressure) to be absorbed
19 Something buzzing around woman in tropical country (6)
BELIZE Thank goodness the “something buzzing” is the busy BEE. LIZ is your random woman
21 Cook squeezes one end of rubber stopper (5)
BRAKE Cook is BAKE, select one (either) end of rubber and insert. That sort of stopper.
24 Programme that’s drivel, quietly being dropped (3)
APP In a clue which seems to advocate dropping a P (quietly) you end up with two of ‘em. Drivel is PAP, and the first P drops one or two spaces. No-one will know which you chose