Ban cars moving round rear of Greek eatery (5,3)
I believe the answer is:
snack bar
'eatery' is the definition.
(thesaurus)
'ban cars moving round rear of greek' is the wordplay.
'moving' indicates an anagram.
'round' means one lot of letters goes inside another.
'rear of' suggests the final letters.
The last letter of 'greek' is 'k'.
'ban'+'cars'='bancars'
'bancars' with letters rearranged gives 'snacbar'.
'snacbar' placed around 'k' is 'SNACK-BAR'.
(Other definitions for snack bar that I've seen before include "Lyons, once?" , "Place where light meals may be had" , "buffet at the roadside" , "Quick fare available here" , "Lunch counter" .)