how to change apple id used with an existing apple music subscription?

Purchases and subscriptions and apps cannot be migrated among Apple IDs.

Cancel the subscription under the old, and start a new subscription under the new.

Or if the Apple Music subscription is the family tier and not an individual subscription, configure and use Family Sharing.

Do you mean change or edit the primary email used as the AppleID? If so, see -> Change your Apple ID - Apple Support

If you mean use a different existing AppleID, you cannot. Purchases and subscriptions cannot be transferred to another AppleID. You would have to cancel the music subscription and re-subscribe under the different AppleID.