Thanks Falcon for an enjoyable puzzle. Definitions are underlined in the clues.
Across
1 Delicate tennis shot to end barrage (4,6)
STOP VOLLEY : STOP(to end) + VOLLEY(a barrage/a number of, say, bullets discharged at the same time).
Defn: … such that the ball is returned just past over the net.
6 Sign of injury may cause a good deal of alarm (4)
SCAR : “scare”(to cause alarm) minus its last letter(a good deal of …).
9 Tight spot right beside broadcaster’s building (10)
SKYSCRAPER : [ SCRAPE(a tight spot/a difficult situation) + R(abbrev. for “right”) ] placed after(beside) SKY(in the UK, a company broadcasting, mainly, television programmes).
10 Spell “vase” after bit of tuition (4)
TURN : URN(a vase, especially used for storing the ashes of a cremated person, pet, etc.) placed after(after) 1st letter of(bit of) “tuition”
Defn: A period of time.
12 Cheers below deck? (4,3,5)
DOWN THE HATCH : DOWN(lower through) THE HATCH(a trap door in the deck of a ship leading to the space below deck).
Defn: Like “Cheers!”, an expression said as a toast before downing a drink.
15 A nasty boil removed, got rid of (9)
ABOLISHED : A + anagram of(nasty) BOIL + SHED(removed, say, clothes, leaves, etc.).
17 State papers seen by a hospital close to Chicago (5)
IDAHO : ID(short for “identity papers”/identity documents) plus(seen by) A + H(abbrev. for “hospital”) + last letter of(close to) “Chicago“.
Defn: … in the USA.
18 Stock English remark that’s funny (5)
EQUIP : E(abbrev. for “English”) + QUIP(an amusing/funny remark/comment).
19 Terry, thoroughly at home wearing short Roman garment (9)
TOWELLING : [ WELL(thoroughly, as in “your goose is well and truly cooked”) + IN(at home/not out) ] contained in(wearing) “toga”(a Roman garment from olden times) minus its last letter(short …).
Defn: A fabric used especially for towels.
20 Everything you’d expect in article by complete Scottish golfer? (3,4,5)
THE FULL MONTY : THE(article in grammar) plus(by) FULL(complete/entire) MONTY(nickname of Colin Montgomerie, Scottish professional golfer).
24 Barrier in the Tagus knocked over (4)
GATE : Hidden in(in) reversal of(… knocked over) “the Tagus“.
25 Consider intentional (10)
DELIBERATE : Double defn: 1st: To think carefully about.
26 Function of list, reportedly (4)
ROLE : Homophone of(…, reportedly) “roll”(a list as in “the electoral roll”).
27 Evaluation fools blokes in street (10)
ASSESSMENT : ASSES(fools) + [ MEN(blokes) contained in(in) ST(abbrev. for “street”) ].
Down
1 Band, southern, has reformed (4)
SASH : S(abbrev. for “southern”) + anagram of(… reformed) HAS.

2 Just left out by variety of agate (4)
ONYX : “only”(just/nothing more) minus(… out) “l”(abbrev. for “left”) + X(by/multiplied by, as in “2 by 2 is 4).

3 Australian state having choice fruit (8,4)
VICTORIA PLUM : VICTORIA(state in south-eastern Australia) plus(having) PLUM(choice/extremely desirable).
4 Gain knowledge of Shakespearean king and knight (5)
LEARN : LEAR(the king in Shakespeare’s play, King Lear, of course) plus(and) N(abbrev. for “knight” in chess notation).
5 Watch programme that includes commercial for a cosmetic (9)
EYESHADOW : EYE(to watch/to look at with interest) + SHOW(a programme, say, on television) containing(that includes) AD(abbrev. for “advertisement”/a commercial).
7 Jazz musician, number one in foundation (5,5)
COUNT BASIE : COUNT(to number/to add up) + [ I(Roman numeral for “one”) contained in(in) BASE(the foundation/the bottom support) ].
The Count and his Orchestra:

8 Practice gallop finished (3-7)
RUN-THROUGH : RUN(to gallop like a horse does) + THROUGH(finished/ended, as in “we’re through!”).
11 Solicitors’ mail? (5,7)
CHAIN LETTERS : Cryptic defn: What some solicitors/canvassers, of say, business schemes might possibly use to spread the word.
13 Daily row about golf figure who’s less powerful than he looks? (5,5)
PAPER TIGER : PAPER(a daily/a newspaper published daily) + TIER(a row/one of a series of rows placed one above the other) containing(about) G(letter represented by “golf” in the phonetic alphabet).
14 Massive memorial by a lake (10)
MONUMENTAL : MONUMENT(a memorial/a structure erected to commemorate someone or something) plus(by) A + L(abbrev. for “lake”).
16 Tall story swallowed by others abroad who offer accommodation? (9)
HOTELIERS : LIE(a tall/unbelievable story) contained in(swallowed by) anagram of(… abroad)OTHERS.
21 Nothing charged for fruit (5)
OLIVE : O(letter representing 0/nothing) + LIVE(charged with electricity/connected to a source of electric current).
22 Fabric: expert after lengths (4)
LACE : ACE(an expert/one very proficient in something) placed below(after, in a down clue) L(abbrev. for “lengths”).
23 Wager about singular former football star (4)
BEST : BET(a wager) containing (about) S(abbrev. for “singular”).
Answer: George, former football star.
Not too difficult but a pleasant solve, with STOP VOLLEY and THE FULL MONTY my favourites and a reminder of Wimbledon and The Open.
Thanks for the picture of a piece of ONYX. I’ve learnt something, as I always thought it was predominantly a black stone (or maybe ‘mineral’ is the correct terminology) but clearly not.
Thanks to Falcon and scchua
I was convinced that it was Drop Volley in 1ac and so failed to solve 1d. As a tennis player, I’ve never heard Stop Volley being used. Otherwise a enjoyable solve.
Thanks Falcon and scchua
A lightning solve today and good to finish on the day of publication for a change. Like contrapunctus@2, I had always referred to that shot as a ‘drop volley’ but finding SASH as my first one in, stopped that in its tracks – fortunately had heard of the alternative name as well.
Nice to see my home state mentioned and it helped as I didn’t know the fruit at all.
Finished in the SW corner with THE FULL MONTY, GATE and ROLE the last few in
Thanks to Falcon and scchua. Lots of fun. I’m another who has never come across STOP VOLLEY but that was clearly the solution. Similarly, I discovered there was an anchovy pear tree (that answer clearly did not parse), but once I got VICTORIA PLUM everything else followed. I know George BEST from previous puzzles but had to consult Google to be certain that MONTY was the nickname of a Scottish golfer.