An eminently 'do-able' QC which should have been quicker but I got held up with the many anagrams.
9 minutes still means on the quick side for me. The same (but different) devices being used in adjacent clues 5/9ac and 17/18dn seemed unusual - let me know if this isn’t.
1. Government department having little right to visit filthy home (8)
MINISTRY - little (MINI), right (R) visiting (inside) filthy home (STY). Thanks to Oink for the trademark.
5. Revolutionary goes beyond mark (4)
SPOT - goes beyond (tops - SPOT - as it’s revolved).
9. Old Nick survived in recession (5)
DEVIL - survived (lived - DEVIL - as it’s in recession).
10. Minister shown round a nuclear facility (7)
REACTOR - minister (RECTOR) round a (A).
11. Girl that’s fond of climbing walls? (3)
IVY - seems to be a double/cryptic definition.
12. Pasty-faced saint in eastern land (9)
PALESTINE - pasty-faced (PALE), Saint (ST), in (IN), eastern (E).
13. A stream round university, reddish brown (6)
AUBURN - a and stream (A BURN) around university (U).
15. Accommodate head of state in Ritz perhaps — or somewhere cheaper? (6)
HOSTEL - (S)tate accommodated inside Ritz perhaps (HOTEL).
17. Furious at airline, among other things (5,4)
INTER ALIA - anagram (furious) of AT AIRLINE.
19. I must leave a hairy creature still (3)
YET - I (I) leaving hairy creature (YET)i.
20. Anticipate knocking back cider in exercise class (7)
PREDICT - cider backwards (REDIC) in exercise class (PT).
21. Article penned by Her Majesty? It might send you to sleep (5)
ETHER - article (THE) penned by Her Majesty (ER).
22. Beast of burden carrying north American (4)
YANK - beast of burden (YAK) carrying north (N).
23. Plump for suet pudding (4-4)
ROLY-POLY - double definition.
1. Island, one featuring in a dream, fantastically (7)
MADEIRA - one (I) featuring inside an anagram (fantastically) of A DREAM.
2. Labourer’s van heading north, visibly empty (5)
NAVVY - van heading north (upwards - NAV), (V)isibl(Y).
3. Picture only you could have painted? (4-8)
SELF-PORTRAIT - cryptic definition.
4. Group occasionally runs by a lake in the country (5)
RURAL - g(R)o(U)p, runs (R) by a and lake (A L).
6. Fan of country found in shop at Rio terminal (7)
PATRIOT - found in sho(P AT RIO T)erminal.
7. Succinct poem needs new beginning (5)
TERSE - poem - verse - with the v replaced by t (TERSE).
8. Is OAP Stanley bursting with enthusiasm? (12)
PASSIONATELY - anagram (bursting) of IS OAP STANLEY.
14. Very cold November for a marsh bird (7)
BITTERN - very cold (BITTER), November (N).
16. GI truly sorry in ceremony (7)
LITURGY - anagram (sorry) of GI TRULY.
17. Suggest in straightforward manner son must leave (5)
IMPLY - in straightforward manner s(IMPLY) son (S) leaving.
18. Very drunk bishop knocked out — it’s all down to chance (5)
LOTTO - very drunk b(LOTTO) with bishop (B) leaving.
19. Brute’s cry of excitement (5)
YAHOO - double definition. The first is a crude, brutish person - with the terms origin from C18: from the name of a race of brutish creatures resembling men in Jonathan Swift's Gulliver's Travels (1726). The second is what you may exclaim on completing this QC.