Having left church, heads off with a stagger (5)
I believe the answer is:
lurch
'a stagger' is the definition.
(I know that stagger can be written as lurch)
'having left church heads off' is the wordplay.
I cannot quite see how this works, but
'left' could be 'l' (common abbreviation) and 'l' is found within the answer.
'church' could be 'rc' (abbreviation for Roman Catholic) and 'rc' is found in the answer.
This explanation may well be incorrect...
'with' is the link.
Can you help me to learn more?
(Other definitions for lurch that I've seen before include "Stagger; abandoned, if left in it" , "Abrupt uncontrolled movement - something not to be left in?" , "Walk with an unsteady uneven gait" , "Sudden unsteady move" , "in which the abandoned may be left" .)