Father is at home - but it hurts! (4)
I believe the answer is:
pain
'it hurts' is the definition.
(I've seen this in another clue)
'father is at home' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'is at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'pa'+'in'='PAIN'
'but' is the link.
(Other definitions for pain that I've seen before include "Unpleasant sensation" , "Sensation of acute discomfort" , "Hurt feeling" , "Suffering, ache" , "Tiresome figure" .)