Do I have to have my iTunes library saved on my phone to have the songs and playlists listed?

[user-removed]

Hi, I hope this is the right place to ask this, I really need an answer.
I recently upgraded from "iPhone 6S 64gb" to "iPhone 7S plus 32gb" and I'm struggling with the lack of space!
Do I have to have all my songs synced to my phone with iTunes in order for them to appear in Spotify?
I have about 15GB of music and I'm struggling to cut down space to migrate to my new phone.
I hope I've made the question clear enough, pleeease help me?!