Dad not right in the head (4)
I believe the answer is:
pate
'head' is the definition.
(thesaurus)
'dad not right' is the wordplay.
'dad' becomes 'pater' ('pater' can be a synonym of 'dad').
'not' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'pater' with 'r' taken out is 'PATE'.
'in the' acts as a link.
(Other definitions for pate that I've seen before include "Meat paste, perhaps de fois gras" , "Meat paste, maybe de fois gras" , "chef's preparation" , "Tasty meat paste, maybe de foie gras" , "chef's item" .)