ACROSS
9 Doubtful learner leaves relative at home holding art composition (9) 
UNCERTAIN - Doubtful (def) from UNC(L)E (learner leaves relative) IN (at home) holding RTA (anagram=composition of ART)

10 One replacing foe's last evacuation aid (5) 
ENEMA - evacuation aid (def) from ENEM(Y) (foe replaces last

11 Candid in speech about old currency (5) 
FRANC - old currency (def) from homophone (in speech) of FRANK (candid)

12 Spiritual sung naked with drunken lord and lady on vacation(9) 
UNWORLDLY - Spiritual (def) from sUNg (sung naked) W (with) ORLD (anagram=drunken of LORD) and LY (lady on vacation)

13 Different section of Joshua not heresy (7) 
ANOTHER - Different (def) from section of JoshuA NOT HEResy

14 Irritates the French after row (7) 
RANKLES - (def) from LES ('the' in French) after RANK (row)

16 Annoyance of keeper losing head (5) 
ANGER - Annoyance (def) from (R)ANGER (keeper losing head)

18 Move quickly in dance (3) 
HOP - Move quickly (def) dance (def)

19 Bit English egg part(5) 
WHITE - egg part (def) from WHIT (bit) E (English)

21 Food with the German soup(7) 
CHOWDER - soup (def) from CHOW (food) with DER ('the' in German)

22 Finding fault with part of leaf chopped in empty bag (7) 
BLAMING - Finding fault with LAMIN(A) (part of leaf choppedi) in BG (empty bag)

24 Lions come prowling; one of these(9) 
SEMICOLON - ; one of these (def) from anagram (prowling) of LIONS COME

26 Old church's leader (short priest) to surpass (5) 
EXCEL - to surpass (def) from EX (old) C (church's leader) EL(I) (short priest)

28 Gas bubbling up in casino next-door (5) 
XENON - Gas (def) from reversal (bubbling up in) casiNO NEXt-door

29 Athlete shows piece (9) 
SPORTSMAN - Athlete (def) from SPORTS (shows) MAN (piece)

DOWN
1 Blow fife oddly after turning up (4) 
PUFF - Blow (def) from FiFe (fife oddly) after PU (turning up)

2 Book of the month "Floating on Bottomless River" (6) 
OCTAVO - Book (def) from OCT (the month) Floating on AVO(N) (bottomless river)

3 Explorer drunk cider around that place (4,3,3) 
ERIC THE RED - Explorer (def) from ERIC D (anagram  =drunk of CIDER) around THERE (that place)

4 TV oil baron drinking Spanish water in British car (6) 
JAGUAR - British car (def) from JR (Ewing - TV oil baron) containing (drinking) AGUA (water in Spanish)

5 Flower presently in small, small quantity of liquid (8) 
SNOWDROP - Flower (def) from NOW (presently) in S (small) DROP (small quantity of liquid)

6 Salty drop of drink? Right! (4) 
TEAR - Salty drop (def) from TEA (drink) R (Right)

7 Fresh food shop announced in city (3,5) 
NEW DELHI - city (def) from homophone (announced) of NEW (fresh) DELI (food shop)

8 Feeling sick without question you said but free from pain (4) 
EASY - free from pain (def) from (QU)EASY (feeling sick  minus (without) Q (question) U (you said))
  
13 A state leader in Turkey (3) 
AGA - leader in Turkey (def) from A GA (state - GA for Georgia)

15 Paper providers are modern men around South Africa  (10) 
NEWSAGENTS - Paper providers (def) from NEW (modern) GENTS (men) around SA (South Africa) 

17 Soil found in spice Queen's dropped at dusk (8) 
GLOAMING - dusk (def) from LOAM (soil) found in GING(ER) (spice less ER (Queen's dropped))

18 Innocent leader of Hussars to provide fewer guns(8) 
HARMLESS - Innocent (def) from H (leader of Hussars) ARM LESS (to provide fewer guns)

20 String in, say, chicken product (3) 
EGG - chicken product (def) from G (string) in EG (say)

22 Sweet doubly good in France (6) 
BONBON - sweet (def) from BON BON (good in French) twice (doubly)

23 Revenue from setter popular with company before (6) 
INCOME - revenue (def) from IN (popular) with CO (company) before ME (setter) 

24 Desirable old flame living in outskirts of Sydney (4) 
SEXY  - Desirable (def) from EX (old flame) in living in SY (outskirts of SydneY)

25 Stick article in church (4) 
CANE - Stick (def) from AN (article) in CE (church)

27 Granted it's fast (4) 
LENT - Granted (def) fast (def)