Only devices running iOS version 11 or later can display animated GIFs in the photos app. If you are not using use the iOS 11, upgrade it.
If you can't upgrade to iOS11 for some reason, it is recommended to install the 'ImgPlay' app. 'ImgPlay' is another app we develop for a view to animated gifs saved in the photos app; it's a free app, and very easy to use.
Shortcut to download link.