The Vodafone Smart Tab 4 has a clock and weather widget that looks like this:

I accidentally deleted the widget, and I cannot find it in the widget list.

What's the name of this app? Where can I find it?

Do this (at your own risk) if that's a default widget came along with OS because those widgets are unrecoverable once deleted.

1 Perform a backup of your important data (remember 'not the settings') in the Tab to a PC or Cloud.

2 Then do a "Hard Reset" of Tab. (Every handset has a unique way to do a hard reset. So Google it.)

3 Tab will be reset to its initial state of course.

4 Restore backup again.

-This is bad idea if you have large amounts of important/sensitive data on your Tab and also ignore this answer if that is not a default widget-

This looks like a lock screen widget, rather than a home screen one. It won't appear in the widget selector - instead, you'll need to re-add it to your lock screen. I'm not sure what the process is on the Smart Tab series, but it's probably in your Settings menu, somewhere having to do with Lock Screen.