Experienced judge’s trip of a lifetime? (4)
I believe the answer is:
hadj
'trip of a lifetime?' is the definition.
(Muslim pilgrimage)
'experienced judge's' is the wordplay.
'experienced' becomes 'had' (have can mean to experience or go through).
'judge' becomes 'j' (abbreviation for judge).
'had'+'j'='HADJ'
(Other definitions for hadj that I've seen before include "Muslim pilgrimage" , "once-in-a-lifetime trip?" , "Religious observance" , "Once in a lifetime experience, perhaps" , "Muslim religious journey to Mecca" .)