I completed this puzzle in 7 minutes. There are three or four clues that I'd guess may present some difficulties but the majority lead to everyday words and are straightforward in their construction. With those solved there should be enough checking letters to provide a way into the other answers. Here's my blog.
As usual definitions are underlined in bold italics, {deletions are in curly brackets} and [anagrinds, containment, reversal and other indicators in square ones]
Across
1
Catch sight of son with trophy (4)
SPOT - S (son), POT (trophy)
4
Fellow bachelor, not carrying as much weight (8)
BLIGHTER - B (bachelor), LIGHTER (not carrying as much weight). B on its own as abbreviation for "bachelor" is sanctioned by Chambers but not by the other usual sources (Concise Oxford and Collins Dictionary). There is, or was, allegedly at one time a list of approved single-letter abbreviations for Times puzzles but I've never seen it.
8
Poor relation from the east (8)
ORIENTAL - Anagram [poor] of RELATION
9
Partner in defeat on board (4)
MATE - Two definitions, the second with reference to chess
10
Common sense required to enclose right legal document (4)
WRIT - WIT (common sense) encloses R (right)
11
Welsh barman I treated after onset of cold (8)
CAMBRIAN - C{old}[onset], anagram [treated] of BARMAN I. C is a common enough abbreviation of "cold" so it was not strictly necessary to have the deletion signalled by "onset" here, but it gives us a smoother surface reading.
12
Process messy fluid: about time (6)
SYSTEM - Anagram [fluid] of MESSY containing [about] T (time)
14
Gentle and kind, leader of government in African country (6)
BENIGN - G{overnment} [leader] in BENIN (African country)
16
Usual / colours (8)
STANDARD - Two definitions, the second with reference to flags
18
One preparing hard for test pulls over (4)
SWOT - TOWS (pulls) reversed [over]
19
Primate drawing in small recess in a church (4)
APSE - APE (primate) encloses [drawing in] S (small). A word I learnt in my earliest attempts at cryptic solving that still comes up regularly.
20
A female, smooth-spoken and well-to-do (8)
AFFLUENT - A, F (female), FLUENT (smooth-spoken)
22
Check on board earlier vessel (8)
SCHOONER - CH (check - chess) contained by [on board] SOONER (earlier). A type of ship or a drinking vessel perhaps, popular particularly amongst drinkers of sherry..
23
Father, eastern church leader (4)
POPE - POP (father), E (eastern)
Down
2
Paint a picture of harbour and fish (7)
PORTRAY - PORT (harbour), RAY (fish)
3
Inside centre, a trained nurse (5)
TREAT - Hidden [inside] {cen}TRE A T{rained}
4
Club's bill raised (3)
BAT - TAB (bill) reversed [raised]. Who's going to be the first to say it?
5
Is priest evil in Asian capital? (9)
ISLAMABAD - IS, LAMA (priest), BAD (evil)
6
Baseball score in series (4,3)
HOME RUN - HOME (in), RUN (series)
7
More in next race (5)
EXTRA - Hidden in {n}EXT RA{ce}
11
What in return? (4,5)
COME AGAIN - Two definitions, the first as in "Pardon?"
13
Hybrid fruit beginning to grow in adapted lean-to (7)
TANGELO - G{row} [beginning] in anagram [adapted] of LEAN-TO. This turned up only last Friday in the main puzzle and prompted one of the regulars (Dr Thud) to ask: "Has anyone ever actually seen a TANGELO? I have only ever seen them offered in crosswords". I can't say I've ever seen one but before crosswords I leant the word from Countdown where it seems to turn up every week.
15
Adult class includes disheartened women (5-2)
GROWN-UP - GROUP (class) contains [includes] W{oma}N [disheartened]. I don't think we often have "both end" deletions in the QC so this may be a new device to some.
17
Subject to endless choice (5)
TOPIC - TO, PIC{k} (choice) [endless]
18
What feller leaves behind is puzzle (5)
STUMP - Two definitions, the first with reference to tree-felling.
21
Conifer, solid, clipped (3)
FIR - FIR{m} (solid) [clipped]