Chase knight into building (4)
I believe the answer is:
hunt
'chase' is the definition.
(hunting is a kind of chasing)
'knight into building' is the wordplay.
'knight' becomes 'N' (chess abbreviation).
'into' is an insertion indicator.
'building' becomes 'hut' (type of small building).
'n' going inside 'hut' is 'HUNT'.
(Other definitions for hunt that I've seen before include "F1 driver" , "Racing driver" , "Pursue quarry" , "Organised search" , "Search (with dogs?)" .)