Promise to give a hand to (7)

I believe the answer is:

betroth

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

'a hand to' is the definition.
I can't judge whether this definition defines the answer.

'promise to' is the wordplay.
'promise' becomes 'bet' (betting is a kind of promising).
'to' becomes 'roth' (I can't justify this - if you can you should believe this answer much more).
'bet'+'roth'='BETROTH'

'give' acts as a link.

Can you help me to learn more?

(Other definitions for betroth that I've seen before include "Engage to be married" , "Plight" , "Promise to marry" , "contract" , "Promise to match" .)

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.