Possible earl in Gateshead, having a close look (7)
I believe the answer is:
peering
'having a close look' is the definition.
(to peer at something is to examine it closely)
'possible earl in gateshead' is the wordplay.
'possible earl' becomes 'peer' (earl is a type of peer).
'gateshead' becomes 'g' (head letter of 'gates').
'peer'+'in'+'g'='PEERING'
(Other definitions for peering that I've seen before include "Looking closely" , "Looking searchingly" .)