Religious adherent's tunic regularly appeared in joke (6)
I believe the answer is:
jesuit
'religious adherent's' is the definition.
(member of the Society of Jesus)
'tunic regularly appeared in joke' is the wordplay.
'regularly appeared' means one should take alternating letters (I've seen 'regularly appearing' mean this).
'in' indicates putting letters inside.
'joke' becomes 'jest' (synonyms).
The alternate letters of 'tunic' are 'ui'.
'ui' placed inside 'jest' is 'JESUIT'.
(Other definitions for jesuit that I've seen before include "Eg, St Ignatius Loyola" , "One in Loyola's order" , "Member of the order founded by St Ignatius Loyola and St Francis Xavier" , "Member of RC order" , "Catholic priest" .)