Fathead going up a tree? (3)

I believe the answer is:

sap

I'm a little stuck... Click here to teach me more about this clue!

'fathead' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps there's an association between them I don't understand?

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for sap that I've seen before include "tunnel" , "Plant's fluid" , "Moisture in wood of a tree" , "Imbecile" , "It's plant juice, idiot" .)

I've seen this clue in the Evening Standard.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.