Just then, left city in Cambridgeshire (6)
I believe the answer is:
solely
'just' is the definition.
(solely means just or only)
'then left city in cambridgeshire' is the wordplay.
'then' becomes 'so' (both can mean 'therefore' or 'in that case').
'left' becomes 'l' (common abbreviation).
'city in cambridgeshire' becomes 'ely' (I've seen this before).
'so'+'l'+'ely'='SOLELY'
(Other definitions for solely that I've seen before include "Singularly" , "Exclusively, only" , "nowhere else?" , "alone" , "Singly" .)