I agree with Tennen, except that I believe it is 24 months since you last received the last bonus. Someone in my extended family closed a Premier account and opened a new one two months later and got the sign-up bonus. The free night certificate stayed in the IHG account even after the card was closed.

Also, I suggest heeding Tennen's advice on PC to Traveler. I cannot confirm that Traveler gets 4th night free, but holding the Traveler card allows one to apply for a new Premier and then PC back to Premier if the application is denied. I see no reason to hold the Traveler card as well as the Premier, so I would suggest closing the Traveler if a new application for Premier is approved.