Running after Charles in Gateshead (7)
I believe the answer is:
chasing
'running after' is the definition.
(I've seen this before)
'charles in gateshead' is the wordplay.
'charles' becomes 'chas' (shortened form).
'gateshead' becomes 'g' (head letter of 'gates').
'chas'+'in'+'g'='CHASING'
(Other definitions for chasing that I've seen before include "Running after" , "work by engraver" , "Pursuing" .)