Conrad State 30 and Physician Access Reauthorization Act This bill modifies the Conrad 30 Waiver program, which incentivizes qualified foreign physicians to serve in underserved communities. It also extends statutory authority for the program through FY2021. Aliens coming to the United States under a J-1 nonimmigrant visa to receive medical training typically must leave the country and reside for two years abroad before being eligible to apply for an immigrant visa or permanent residence. The Conrad program waives this requirement for individuals who meet certain qualifications, including serving for a number of years at a health care facility in an underserved area. The bill increases the number of waivers that a state may obtain each fiscal year from 30 to 35 if a certain number of waivers were used the previous year, and provides for further adjustments depending on demand. An alien physician may be employed at an academic medical center to meet the Conrad program's employment requirements if the alien's work is in the public interest, even if the medical center is not in an underserved area. Employment contracts for alien physicians under the Conrad program shall contain certain information, such as the maximum number of on-call hours per week the physician shall have to work. Certain alien physicians (along with the physician's spouse and children) shall be exempt from the direct annual numerical limits on immigration, including those physicians that have met certain requirements related to visas for physicians to serve in underserved areas.