Travel around the borders of Eccles and live (6)
I believe the answer is:
reside
'live' is the definition.
(residing is a kind of living)
'travel around the borders of eccles' is the wordplay.
'travel' becomes 'ride' (ride is a kind of travel**).
'around' means one lot of letters goes inside another.
'the borders of' suggests removing the centre.
'eccles' with its centre removed is 'es'.
'ride' placed around 'es' is 'RESIDE'.
'and' is the link.
(Other definitions for reside that I've seen before include "Dwell permanently" , "Dwell, be present (in)" , "Occupy a place" , "Live (in a place)" , "'Live, dwell (6)'" .)