Bishop runs to a vessel (4)
I believe the answer is:
boat
'vessel' is the definition.
(boat is a kind of vessel)
'bishop runs to a' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'runs' indicates anagramming the letters.
'to'+'a'='toa'
'toa' anagrammed gives 'oat'.
'b'+'oat'='BOAT'
(Other definitions for boat that I've seen before include "Water craft" , "Water transport" , "Water (or gravy) vessel" , "See 1" , "Vehicle for travelling over water" .)