Has old bowler possibly arrived at end of pitch? (4)
I believe the answer is:
hath
'has old' is the definition.
(historical form of 'has')
'bowler possibly arrived at end of pitch?' is the wordplay.
'bowler possibly' becomes 'hat' (bowler is a type of hat).
'arrived at' says to put letters next to each other.
'end of' says to take the final letters.
The final letter of 'pitch' is 'h'.
'hat'+'h'='HATH'
(Other definitions for hath that I've seen before include "Has old" , "Has in an old-fashioned way" , "'The moon . . . . raised her lamp above' (The Lily of Killarney)" .)