Welcome to Android Central! Which phone? The easiest way is to install the Google Photos app on the new phone (if it isn't already there). But if you want to use the stock Gallery app for some reason (e.g., specific editing tools), then you may have to download individual photos from your Google Photos cloud to the phone. Using the Google Photos app, select the photo, tap Menu, then Save to Device. It should then show up in the stock Gallery app.
Some stock Gallery apps have the ability to access the Google Photos cloud, so let us know which phone you have.