Old player that you’d not want in your side finally vetoed by president (9)

'old player' is the definition.
(actress Sybil Thorndike, 1882-1976)

'that you'd not want in your side finally vetoed by president' is the wordplay.
'that you'd not want in your side' becomes 'thorn' (as in a thorn in one's side).
'finally' indicates one should take the final letters.
'by' says to put letters next to each other.
'president' becomes 'ike' (nickname of Dwight Eisenhower).
The final letter of 'vetoed' is 'd'.
'thorn'+'d'+'ike'='THORNDIKE'