Linger around front of shrine, following church leader's ambulatory (8)
I believe the answer is:
cloister
'ambulatory' is the definition.
(I've seen this before)
'linger around front of shrine following church leader's' is the wordplay.
'linger' becomes 'loiter' (synonyms).
'around' indicates putting letters inside.
'front of' suggests taking the first letters (the letter at the front of the word).
'following' says to put letters next to each other.
'leader' indicates taking the first letters.
The initial letter of 'shrine' is 's'.
The initial letter of 'church' is 'c'.
'loiter' placed around 's' is 'loister'.
'loister' put after 'c' is 'CLOISTER'.
(Other definitions for cloister that I've seen before include "Covered monastic walkway" , "sacred enclosure?" , "Cathedral's covered walk" , "Covered walk in monastery or convent" , "Covered walk in religious institution" .)