Around Michigan, remains of the strictly old-fashioned sect (5)
I believe the answer is:
amish
'the strictly old-fashioned sect' is the definition.
'around michigan remains' is the wordplay.
'around' indicates putting letters inside.
'michigan' becomes 'mi' (state letters).
'remains' becomes 'ash' (I've seen this before).
'mi' inserted inside 'ash' is 'AMISH'.
'of' is the link.
(Other definitions for amish that I've seen before include "US religious community" , "American follower of the Mennonite religion" , "Of US Mennonites" , "Member of a sect" , "sectarian" .)