Is this about the Apple TV+ subscription, or a different subscription for a different content provider?
Some US streaming services only allow streaming within the US borders. Some others may allow streaming is select other countries. See their terms of service for details. That may include Apple TV app channels by third parties.
Netflix and Amazon Prime Video are exceptions that have near worldwide coverage for subscribers, although there may be some differences in the local catalog by country.
If you set your Apple Account to a different country or region, then that requires that all subscriptions with payment through Apple are ended at the moment of change. It would also require a different payment method, local to the new country or region. Additionally, Family Sharing isn’t supported internationally; all group members should have their account set to the same country.
But if your Apple Account is still set to the US, with a linked US payment method, then a subscription like Apple TV+ is expected to work in other countries as well. No guaranties though.
Aside from moving countries, subscription fees are paid for the upcoming period, not the past period.
Verify that you signed in with the Apple Account that has the Apple TV+ subscription linked to it. New accounts or different accounts wouldn’t get access to the same. For potentially multi-user devices like Apple TV boxes, it is about the chosen active account, not the device per se.