This should be a very simple process, and upgrading to ATP during recurrent checkrides is a common occurrence. With a 737 type rating, you've already "flown" the ATP checkride, the routine will be nearly identical to the initial type-ride or any recurrent checkrides. You will, of course, need to have fulfilled all ATP requirements per FAR Part 61, Subpart G (link:
Electronic Code of Federal Regulations: (1500 hrs total time, etc.) and passed the ATP written exam. Then, as you guessed, a simple call to your sim center should get you on the easy path for this upgrade.
Good luck!