I am going by the assumption that the new phone has the new Gmail. So here are two ways you can go about it.
Even though the device has a new gmail, you can have more than one google account on a phone. So after adding the new one, add another account, which would be the old one.
Once done, log in to that old account and download the photos to the phone. Once you have downloaded them all, log out of that account and back into the other one. (if you logged out of the new one that is).
Now all you need to do is upload them all to the new account.
This one requires access to a computer. Because of that it is not only faster, but doesn't require you have enough room on the phone for all the photos.
From the computer, log into the old google account and download the files to an empty folder on the computer.
Once downloaded, log out of that account and then log into the new one. Upload the photos and you should be good.