Fight in Greek city-state? No thanks! (4)
I believe the answer is:
spar
'fight' is the definition.
(sparring is a kind of fighting)
'greek city-state? no thanks' is the wordplay.
'greek city-state?' becomes 'sparta' (I've seen this in another clue).
'no' suggests deleting specific letters.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'sparta' with 'ta' removed is 'SPAR'.
'in' is the link.
(Other definitions for spar that I've seen before include "Act as boxer" , "Crystalline mineral" , "Fight - something probably rigged?" , "Train at boxing; mineral" , "A mineral; nautical pole" .)