Weave mine around city (5)
I believe the answer is:
plait
'weave' is the definition.
(I know that plait is a more specific form of the action the weave)
'mine around city' is the wordplay.
'mine' becomes 'pit' (as in a mining pit).
'around' means one lot of letters goes inside another.
'city' becomes 'LA' (Los Angeles).
'pit' enclosing 'la' is 'PLAIT'.
(Other definitions for plait that I've seen before include "Braided hair" , "Weave; queue" , "Hair braid" , "Interweave (lengths of hair)" , "Hairdo formed by braiding" .)