New device how do I transfer apple music onto it?

I already have subscribed to apple music for one person on my phone, but I am unable to access from an old MacBook Pro I got from someone in my family sharing. I have already logged into my own icloud account onto my acquired Mac but when I open iTunes and go to my music library it doesn't show that I have apple music. It instead shows the different subscription plans I can buy. What do I need to do to get the apple music I have already purchased onto my MacBook?