In a fearful state, father's not quite nice (5)
I believe the answer is:
panic
'in a fearful state' is the definition.
I can't tell whether this definition defines the answer.
'father's not quite nice' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'not quite' means to remove the last letter (most but not all of the word).
'nice' with its final letter removed is 'nic'.
'pa'+'nic'='PANIC'
Can you help me to learn more?
(Other definitions for panic that I've seen before include "Greek god" , "Lose one's cool" , "much unease" , "Frenzy" , "Lose the head, yield to fear" .)