ICAO doesn't issue licenses, your local CAA/DGCA/FAA issues a licence that meets ICAO standards. The FAA ATP is an ICAO license just like a British CAA ATPL is.
The question is, do you want a FAA certificate based on your foreign license or a stand alone FAA certificate. The stand alone is straight forward, you've got the time so medical, written and checkride but unless you take the check in a 320 sim, no 320 type.
To get a FAA certificate based on your foreign license, check here:
Airmen Certification: Verify the Authenticity of a Foreign License, Rating, or Medical Certification
You understand the process, get your CAA to validate your license, take the instrument knowledgeg test for foreign pilots and a checkride.