How do you give a gift subscription of Apple Music?
How do you give a gift subscription of Apple Music to someone who has an iPod Touch?
iPod Touch
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Since an Apple Music subscription requires a continuous monthly charge, I doubt that you can do that. However, you can gift them an Apple gift card for whatever amount you want to get them started. See the "Email a gift card" section in:
Send a gift from the App Store, iTunes Store, Apple Books, and more - Apple Support