There is no such thing as an "ICAO license", so I assume you are asking about converting from a non-FAA license to a FAA certificate on the basis that both countries' licenses are ICAO compliant.
If you will not meet the requirements to hold a FAA ATP Certificate by the time you are ready for your practical test, then you will need to take the Commercial Pilot certificate written test. Unlike some other jurisdictions, the ATP written does not "cover" the commercial pilot certificate.
The only certificate that requires 1500 hours is the ATP. As markerinbound said, you can add a type rating to anything private pilot and above.