Father Norm went out west (6)
I believe the answer is:
parent
'father' is the definition.
(I know that father can be written as parent)
'norm went out west' is the wordplay.
'norm' becomes 'par' (I've seen this in another clue).
'out' suggests deleting specific letters.
'west' becomes 'W' (abbreviation).
'went' with 'w' taken out is 'ent'.
'par'+'ent'='PARENT'
(Other definitions for parent that I've seen before include "Mother or father or what they do" , "Immediate ancestor" , "person responsible for children" , "governor, for example" , "Raise" .)