Took Jack for pilgrimage (4)
I believe the answer is:
hadj
'for pilgrimage' is the definition.
(hadj is a kind of pilgrimage)
'took jack' is the wordplay.
'took' becomes 'had' ('have' can be a synonym of 'take').
'jack' becomes 'J' (playing card abbreviation).
'had'+'j'='HADJ'
(Other definitions for hadj that I've seen before include "One pillar" , "Muslim pilgrimage" , "Muslim religious journey to Mecca" , "Once in a lifetime experience, perhaps" , "A pilgrimage to Mecca, duty of Muslims" .)