Stay with North American president (5)

I believe the answer is:

biden

'american president' is the definition.
(Joe Biden)

'stay with north' is the wordplay.
'stay' becomes 'bide' (biding is a kind of staying).
'with' means one lot of letters go next to another.
'north' becomes 'N' (abbreviation).
'bide'+'n'='BIDEN'

I've seen this clue in The Telegraph.

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.