Old one, possibly a fathead (6)
I believe the answer is:
noodle
'a fathead' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'old one possibly' is the wordplay.
'possibly' indicates anagramming the letters.
'old'+'one'='oldone'
'oldone' is an anagram of 'NOODLE'.
Can you help me to learn more?
(Other definitions for noodle that I've seen before include "strip in the kitchen" , "Form of pasta" , "Egg pasta" , "Simpleton; piece of pasta" , "Foolish person or slangy head" .)