Bird runs away from port (4)
I believe the answer is:
dove
'bird' is the definition.
(dove is a kind of bird)
'runs away from port' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'away from' is a deletion indicator.
'port' becomes 'dover' (English port).
'dover' with 'r' taken away is 'DOVE'.
(Other definitions for dove that I've seen before include "Symbol of peace" , "Mourning, collared, bird" , "Peace lover; bird" , "Pigeon-like bird" , "Bird; advocate of peace" .)