Pursue knight concealed in shed (4)
I believe the answer is:
hunt
'pursue' is the definition.
(I know that hunt is a type of dog)
'knight concealed in shed' is the wordplay.
'knight' becomes 'N' (chess abbreviation).
'concealed in' means one lot of letters goes inside another.
'shed' becomes 'hut' (I've seen this before).
'n' placed within 'hut' is 'HUNT'.
(Other definitions for hunt that I've seen before include "Meet - famous mountaineer" , "Forage" , "Racing driver" , "Search; chase" , "Search (with dogs?)" .)