Imported Posts missing summary text on staging site

Although there’s little chance that something went wrong, first of all make sure that you content is actually there. Just edit a post from your dashboard and make sure it looks like it should,

Now, it looks like you have different themes on you live and staging sites, so it most probably is an issue with your staging theme. It might have its own set of configuration options (check Appearance > Customize), or it might be a bug.

It’s probably best to read the theme’s documentation or contact the theme’s author.