If you had iCloud Photo Library turned on, you can use any computer and log in to www.icloud.com and go to the Photos app there to see if you can see the photos. If so, you can turn iCloud Photo Library on in the new phone and they will sync to it. See: iCloud Photo Library - Apple Support
If you didn't have iCloud Photo Library turned on but possibly did have iCloud backup turned on, you can use the backup to setup the new phone. iCloud: Restore or set up your iOS device from iCloud