Follower recycled tea-cosy - section becoming gilet essentially (7)
I believe the answer is:
acolyte
'follower' is the definition.
(I've seen this before)
I don't understand the remainder of the clue.
(Other definitions for acolyte that I've seen before include "Assistant, follower" , "Assistant to a priest" , "Altar boy" , "Adherent or priest's assistant" , "trainee" .)