You can use a Google Sheets add-on "Photo Gallery" to create a slideshow with Google Slides, from photos in your Drive. You can then insert this slideshow in a site (either classic or new).

1. In Google Drive create a new spreadsheet.

2. Install this Add-on https://support.awesome-table.com/hc/en-us/sections/360001078120-Photo-Gallery

3. Click Add-ons and select Photo Gallery by Awesome table.

4. In the right hand column select a folder in your drive that contains the photos you want in your gallery.

5. Continue to create the slideshow.  

6. When finished click to view the Slideshow that has been created.

7. In your web site in the insert menu click Slides under Google Embeds and select the newly created Slideshow. (Remember to change its sharing to public).

CREDIT: Add-on created by Romain Vialard and there are more instructions on his web site.

"As Picasa / Google Photos has deprecated its slideshow feature, one remaining solution was to add your photos as slides of a Google presentation. But this can be very time consuming if you have many photos! 

Thanks to our add-on, you can simply put all your photos in a Drive folder and we will automatically insert them in a Google Slides presentation that you can embed in any website."

See an example below. Note: on a mobile device the slideshow doesn't start until the viewer clicks on it to open it.

More 2015 TC Summit Pics

Below is an inserted Drive Folder
I got the shared folder URL and inserted it using the by URL section of the Embed function.

Google Album Photos