Run after Charles East (5)
I believe the answer is:
chase
'run after' is the definition.
(I've seen this in another clue)
'charles east' is the wordplay.
'charles' becomes 'Chas' (shortened form).
'east' becomes 'e' (abbreviation).
'chas'+'e'='CHASE'
(Other definitions for chase that I've seen before include "Hurry" , "groove" , "Pursue; decorate (metal) by engraving" , "Pursuit" , "Hound" .)