Fool to go by, scratching head (3)
I believe the answer is:
ass
'fool' is the definition.
(both can mean a stupid person)
'go by scratching head' is the wordplay.
'go by' becomes 'pass' (synonyms).
'scratching head' means to remove the first letter (the word\'s head is removed).
'pass' with its first letter taken off is 'ASS'.
'to' is the link.
(Other definitions for ass that I've seen before include "Titania loved one" , "Trump's behind" , "Idiotic animal" , "slow-witted person" , "Bottom, temporarily" .)