Fool, I note, upset with another fool (6)
I believe the answer is:
nitwit
'fool' is the definition.
(both can mean a stupid person)
'fool i note upset with another' is the wordplay.
I cannot really understand how this works, but
'fool' could be 'twit' (both can mean a stupid person) and 'twit' is found in the answer.
'i' is present in the answer.
'note' could be 'n' (abbreviation) and 'n' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for nitwit that I've seen before include "Twin it with a right eejit" , "Informally, a foolish person, featherbrain" , "Turkey" , "Noodle, numskull" , "Foolish person like humorous louse" .)