Mean street in outskirts of Grimsby (6)
I believe the answer is:
stingy
'mean' is the definition.
(both can mean miserly)
'street in outskirts of grimsby' is the wordplay.
'street' becomes 'st' (abbreviation).
'outskirts of' suggests removing the centre (only letters on the outskirts).
'grimsby' with its centre taken out is 'gy'.
'st'+'in'+'gy'='STINGY'
(Other definitions for stingy that I've seen before include "Painful" , "Mean, niggardly" , "Close" , "Patch of nettles is" , "Parsimonious like nettle?" .)