Can I use a different Apple ID for Apple Music and Apple TV than the one is used to set up the iPad?

AppleTV and Apple Music services will use the AppleID with which you are currently signed-in to iCloud.

i.e., Settings > [Your Name / AppleID]

However, it is possible to sign-in to other services, such as Apple App Store, Messages and FaceTime, with a different AppleID.

So, in context of your explicit question, no, you can’t.

I hope this clarification is helpful to you in resolving any uncertainty as to the AppleIDs that you can use.

I am trying to sign-in to my ipad using one appleID for my icloud services but a different one for the App store. I cant seem to find that way to do that again on my iPad again. I had it setup that way before mistakenly signing out on that ipad. Where can I find instructions to do this?