Dad has some measure of suffering (4)
I believe the answer is:
pain
'suffering' is the definition.
(suffering is pain)
'dad has some measure' is the wordplay.
'dad' becomes 'pa' (both can mean one's father).
'has' means one lot of letters go next to another.
'some measure' becomes 'in' (in is a kind of measure).
'pa'+'in'='PAIN'
'of' acts as a link.
(Other definitions for pain that I've seen before include "Bodily suffering or mental anguish" , "Suffering of body or mind" , "Annoying person" , "Physical discomfort" , "Mental distress" .)