Quick Cryptic No 663 by Hurley

Definitions are underlined, anagrams indicated by [square brackets] and deletions with {curly ones}

Across
8  After time, walk with swaying gait? Nonsense (7)
TWADDLE – T{ime} with WADDLE
9  Values range of small cold beer (5)
SCALE – S{mall} C{old} plus ALE (beer)
10  Paul regularly timid?  Quite the opposite (5)
PUSHY – a semi &lit clue (the whole clue gives the definition), and constructed as follows – P{a}U{l} (regularly, i.e. alternate letters) with SHY (timid) to give something that is the opposite of timid
11  Extremely slick new title for pin used in game (7)
SKITTLE – (extremely, i.e. outside letters) S{lic}K with an anagram (clued by ‘new’) of [TITLE]
12  Poet Stephen one’s seen shopping? (7)
SPENDER – a SPENDER might be seen shopping, and Stephen SPENDER was Sir Stephen Harold Spender CBE, an English poet, novelist and essayist
14  Astonish a parent with variable English (5)
AMAZE – A (a) MA (parent, i.e. mother or MA), Z (variable – the letter Z is often used to represent a variable in an equation) and E{nglish} – put them together and voila, you will AMAZE
15  French writer parking away from university grounds (5)
CAMUS – University grounds are a CAM{p}US.  Remove P{arking} and you get Albert CAMUS, the French philosopher, author and journalist and Nobel laureate (literature) much loved by crossword setters
17  John introduced to cuter refashioned hairstyle (4,3)
CREW CUT – a John in America is what we often call a WC in the UK.  Put WC inside (introduced) an anagram (clued by ‘refashioned’) of [CUTER] to make CREW CUT
19  Manage firm used by Royal Navy in Cheshire town (7)
RUNCORN – RUN (manage) CO (firm) and R{oyal} N{avy}
20  Fish – wonderful (5)
BRILL – a double definition – BRILL is a type of fish and also can mean wonderful amongst the yoof of today (or was that yesterday?)
22  Feel great need for Conservative party? (5)
CRAVE – C{onservative} and RAVE (party)
23  Rugby Union’s followed by Welsh girl and foreign national (7)
RUSSIAN – R{ugby} U{nion}’S followed by SIAN – one of those girl’s names that I struggle to pronounce.  It is equivalent to the English Jane, the Scottish Sheena or the Irish Siobhan, the first two of which are much easier to pronounce

Down

STOP – I took a few minutes to parse this before I spotted that the answer is the first letters (at outset) of S{ports} T{raining} O{ver} P{roblems}
2  Story about silly girl (6)
LASSIE – the story is a LIE, with ASS in for silly.  I’m not sure that the adjective ‘silly’ and the noun ‘ass’ are exactly interchangeable, but ‘ass’ and ‘silly’ are so often associated with each other that I suppose it is OK?
3  Nervous journalist has good year after (4)
EDGY – Journalist is nearly always an ED{itor} in crosswordland, followed in this case by G{ood} Y{ear}
4  Uncle and retirees exercising here? (7,6)
LEISURE CENTRE – straightforward anagram indicated by ‘exercising’ of [UNCLE] and [RETIREES] with the whole clue providing the definition, i.e. a semi &lit
5  In Paris is one friend making approximate calculation (8)
ESTIMATE – EST (French, i.e. what one might say in Paris, for ‘is’) I (one) MATE (friend)
6  Chap painting over slogan (6)
MANTRA – the chap is a MAN and painting is ART with over clueing that the ART is reversed
7  Some defer – ever entirely respectful (8)
REVERENT – cleverly hidden answer in {defe}R EVER ENT{irely}
12  Contest to find out who’ll be first to be fired (4,4)
SACK RACE – an amusing whole clue definition
13  Find out Detective Inspector’s assumed identity (8)
DISCOVER – DIS from D{etective} I{nspector}’S and COVER is an assumed identity, especially in my favourite spy novels
16  Work many do – and when it might start? (6)
MONDAY – another whole clue definition containing an anagram (clued by ‘work), this time of [MANY DO]
18  Greek character with access code to provide money (4,2)
CHIP IN – The Greek character is CHI (the 22^nd letter of the Greek alphabet) and PIN is the access code that we all forget
20  Contemptible centre of operations (4)
BASE – straightforward double definition
21  Join left in Korea’s capital (4)
LINK – L{eft} plus IN (in) plus K{orea’s} capital as in capital letter, rather than capital city