Minister, not well in middle of week, getting wake-up call (8)
I believe the answer is:
reveille
'wake-up call' is the definition.
(military wake-up call played on an instrument)
'minister not well in middle of week' is the wordplay.
'minister' becomes 'rev' (short for reverend).
'not well' becomes 'ill' ('ill' is the opposite to 'well').
'in' is an insertion indicator.
'middle of' means to look at the middle letters.
The middle letters of 'week' are 'ee'.
'ill' inserted into 'ee' is 'eille'.
'rev'+'eille'='REVEILLE'
'getting' acts as a link.
(Other definitions for reveille that I've seen before include "Military signal to wake up" , "Army waking signal" , "Military wake-up call" , "Wake-up signal" , "Bugle call to awaken soldiers" .)