The country or region of your Apple Music subscription is linked to the country or region of your Apple ID, which is based on the listed billing address. You can change the country or region of your Apple ID, but in the process you may loose access to some content from the previous country or region, while in the new country.
When you change the country or region of your Apple ID, you will be asked for a new payment method, which must be valid locally.
Change your Apple ID country or region - Apple Support
If you had any subscriptions, then those will have to be canceled, and may expire soon afterwards. If you want subscriptions to expire sooner, then you can ask the iTunes Store staff for assistance with that.
With a new region for your Apple ID, you can shop in the local iTunes Store, App Store and get an Apple Music subscription for the new region.