Experienced judge's annual trip (4)
I believe the answer is:
hadj
'annual trip' is the definition.
(alternative spelling of Hajj, Islamic pilgrimage)
'experienced judge's' is the wordplay.
'experienced' becomes 'had' (having is a kind of experiencing).
'judge' becomes 'j'.
'had'+'j'='HADJ'
(Other definitions for hadj that I've seen before include "Islamic pilgrimage" , "Once in a lifetime experience, perhaps" , "once-in-a-lifetime trip?" , "Spiritual trip" , "One pillar" .)