my_add_user_cap_for_ticket

add_action(
    'AHEE__EE_Transaction_Processor__update_transaction_and_registrations_after_checkout_or_payment',
    'my_add_user_cap_for_ticket',
    10,
    2
);

function my_add_user_cap_for_ticket(
    $transaction,
    $update_params
) {
    if($transaction->status_ID() != 'TCM') {
        return;
    }
    $registrations = $transaction->registrations();
    foreach($registrations as $registration) {
        if($registration instanceof EE_Registration) {
            if($registration->get('TKT_ID') == 10) { // swap in your ticket ID here - This is for Early Bird Regular Membership
                $user = new WP_User(get_current_user_id());
                if( $user instanceof WP_User ) {
                    $user->add_cap('foo'); // swap in your capability here
                }
                return;
            }
        }
    }
}