Horrible fate with rook chasing (5)
I believe the answer is:
after
'chasing' is the definition.
(I've seen this in another clue)
'horrible fate with rook' is the wordplay.
'horrible' indicates an anagram.
'with' means one lot of letters go next to another.
'rook' becomes 'R' (chess abbreviation).
'fate' with letters rearranged gives 'afte'.
'afte'+'r'='AFTER'
(Other definitions for after that I've seen before include "Searching for" , "At a later time or behind" , "In pursuit of, behind" , "Behind; in quest of" , "Looking for" .)