Move slowly at home and church (4)
I believe the answer is:
inch
'move slowly' is the definition.
(to inch along is to move slowly)
'home and church' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'and' is a charade indicator (letters next to each other).
'church' becomes 'ch' (common abbreviation).
'in'+'ch'='INCH'
'at' is the link.
(Other definitions for inch that I've seen before include "Edge along" , "Creep towards < island" , "Progress slowly" , "Islet (Scots); twenty-five.four mm" , "Creep, edge" .)