Hello Paulerspury,
Thank you for posting in the Apple Support Communities. We understand you're seeing incorrect album artwork after updating to a new phone.
To clarify, is this happening in the Music app specifically? In which view are you seeing this? For example, in Playlists, Albums, Artists, Songs, or all of those?
Does it help if you Restart your iPhone?
Are you using an Apple Music subscription, or are you syncing content from iTunes?
If you use Apple Music, try tapping Settings > Music and turn Sync Library off and back on. If you sync from iTunes, connect your device and uncheck "Sync Music" in your device summary and click Apply, and then re-sync your content to see if this helps: Sync your iPhone, iPad, or iPod using iTunes on your computer
If the issue persists, I recommend that you Contact Apple Support.
Take care.