Skirt around centre of Edinburgh in a taxi
I believe the answer is:
minicab
'a taxi' is the definition.
(I've seen this before)
'skirt around centre of edinburgh' is the wordplay.
'skirt' becomes 'mini' (a mini skirt).
'around' becomes 'ca' (circa).
'centre of' indicates the central letters.
The middle letter of 'edinburgh' is 'b'.
'mini'+'ca'+'b'='MINICAB'
'in' acts as a link.
(Other definitions for minicab that I've seen before include "Car used as taxi" , "It can't be hailed in the street" , "Type of taxi" , "Hired vehicle" , "transport" .)