If you are interested in extending the $4 offer, you can chat with customer care to cancel. They will then offer you to extend the $4 promo for another year.
Just now I received an email from NYT welcoming back to resubscribe. There was an activation link in the email that auto-subscribes you for 1 year at the old $4.00 rate. So I clicked it and resubscribe. Better than having to call CS dealing with a sales pitch.😀 I'll cancel again next year.