Does the iPod Nano have a clock app

According to the User Guide, yes it does: https://manuals.info.apple.com/MANUALS/1000/MA1624/en_US/iPod_nano_2015_user_gui de.pdf

Just to clarify, the nano 7g has a clock function, though not an "app" in the sense that applies to iOS devices such as the iPhone or iPad. The nano clock function tells the time and can be adjusted for timezone, but nothing more.

Actually that is not what the manual indicates (see pgs 43-45).