Left Kay going round ancient city to lie in wait (4)
I believe the answer is:
lurk
'lie in wait' is the definition.
(thesaurus)
'left kay going round ancient city' is the wordplay.
'left' becomes 'l' (common abbreviation).
'kay' becomes 'k'.
'going round' is an insertion indicator.
'ancient city' becomes 'ur'.
'l'+'k'='lk'
'lk' placed around 'ur' is 'LURK'.
'to' is the link.
(Other definitions for lurk that I've seen before include "Lie in wait" , "Hide or wait stealthily" , "Wait in hiding to attack" , "Lie in ambush" , "Wait in ambush" .)