Territory Health Insurance Tax Relief Act of 2019 This bill lowers the annual fee on health insurers, specifically for those insurers that collect premiums from residents in U.S. territories. The annual fee for a health insurer is currently calculated based on the insurer's share of total premiums from the preceding calendar year. The bill excludes premiums paid by residents of U.S. territories from a health insurer's net premiums, but still includes the premiums of such residents in the determination of total premiums from the preceding year, thereby lowering the fee for these insurers. Under current law, the fee is suspended for calendar 2019 (i.e., there is no fee based on premiums from calendar 2018).