Across
Spooner's only visitor died (4,4)
I haven't cracked this one yet — but Fifteensquared have:
definition: ‘to go west’ is to die, or to become lost/destroyed Spoonerism of ‘one guest’=”only visitor”
Where copper needs to go to get old-school jazz fan up for relations? (2,4)
Takes horse say, and climbs rapidly (6,2)
Develop play oddly following cross into goal (6)
I haven't cracked this one yet — but Fifteensquared have:
odd letters from P-[l]-A-[y], following X=”cross”; all inside END=”goal”
Awful Prime Minister is, alas, ultimately missing opposition to growth? (4-11)
I haven't cracked this one yet — but Fifteensquared have:
anagram/”Awful” of (Prim-[ e ] Ministe-[ r ] i-[ s ] ala-[ s ])*, edited thanks to Jay in the comments – with the last/ultimate letters of each word removed/missing with the last/ultimate letter of ala s removed/missing
16a
Sailor into the water – wanting a river to get clean (5,5)
See 15
Suit pursuing net damages somehow getting result from court (4,3,3,5)
I haven't cracked this one yet — but Fifteensquared have:
definition refers to a result on a tennis court MATCH=”Suit”, following anagram/”somehow” of (net damages)*
Using rag as well for ink (6)
Computer equipment from any other business in recession on main road (8)
I haven't cracked this one yet — but Fifteensquared have:
A.O.B. (‘Any Other Business’, in a meeting’s agenda) reversed/”in recession”; after KEY=”main” and followed by RD (road)
Wrong about following number 20's sport (6)
I haven't cracked this one yet — but Fifteensquared have:
definition: solution to 20ac is a tennis phrase SIN=”Wrong” reversed/”about”; following after TEN=”number”
Votes against adopting explosive candidates (8)
Down
Times going after Foreign Office and Chancellor – they're out for blood? (3-4)
I haven't cracked this one yet — but Fifteensquared have:
X=”Times” (e.g. 2×3 / two times three); after FO (Foreign Office), and followed by Jeremy HUNT=UK “Chancellor” of the Exchequer
Adjusting one leg a bit on the table (10)
Fed sons stew (4)
18d
Scientist's flight-component placed on two birds with clipped wings (7,7)
Made during a concert with, say, Robin Williams essentially entering profession (10)
Boots, maybe Hush Puppies' first with zip set in (4)
I haven't cracked this one yet — but Fifteensquared have:
definition: Boots is the name of a chain of pharmacy shops in the UK SH (be quiet, “Hush”) + first letter of P-[uppies]; with O=zero=”zip” inside
Husband joining a navy ship under European control (7)
I haven't cracked this one yet — but Fifteensquared have:
H (Husband) + A (from surface) + RN (Royal Navy); plus SS (steam ship) after E (European)
Relocate to protect independent American cinema (5,5)
I haven't cracked this one yet — but Fifteensquared have:
MOVE HOUSE=”Relocate” around I (independent)
Make merry as poet gets a drink for everyone in shed (4,6)
I haven't cracked this one yet — but Fifteensquared have:
[Philip] LARK IN =”poet” + A ROUND=”a drink for everyone”; with “ in shed” i.e. the letters IN removed
Wall Street's conclusion after forging a paper (7)
I haven't cracked this one yet — but Fifteensquared have:
final letter/”conclusion” of [Stree]-T; after anagram/”forging” of (a paper)*
See 4
Escape in sports car perhaps (7)
Play securing new award (4)
Politician supporting closures from January to March (4)
I haven't cracked this one yet — but Fifteensquared have:
definition: a UK term for a march (e.g. done by a soldier) MP (Member of Parliament, “Politician”) after closing letters to [Januar]-Y [t]-O
Type letters or click words in the clue