You should not rely on the grace period as 'extra time to park'. Your renewed permit will be started from the day after the grace period, if the grace is used.
Parking permits
A grace period of 21 days is in place for all parking permit holders. This means you can display your parking permit for 21 days after the expiry date printed on it. As long as you've submitted your renewal application and you're parked according to the conditions of your current parking permit, you will not receive a fine.