This can be done easily with the custodial wallet, but if you have a non-custodial wallet, you must write a library[1] or use open source scripts[2] that have automatic automation of transactions so that the amount of X is sent every first day of the month at 12:00 and thus you can automatically renew your service.
Sounds like it can work like that, but there is still a problem that in such case the entire subscription process takes place only in client's wallet while the service also needs to collect this data in order to have the correct metrics (which are essential for development of the project's business strategy) . Therefore, for such option the wallet needs to share the data with a service and for the time being I don't see any way to bypass it.