How do I install timer app on Apple Watch?

If you press the digital crown, you should be able to scroll down to the Timers app. It should be preinstalled.

You can add a shortcut to the app as a watch face complication on some watch faces.

Apple Watch Complications: a complete user guide

M1 Mac mini, macOS 15.3.1;  Watch, series 10 GPS-only, watchOS 11.3.1; iPhone 16, iOS 18.3.1; TV 4th Gen, tvOS 18.3; HomePods, audioOS 18.3 and Airport Express w/ Airplay 2

If the default Timers App got deleted somehow, you can download it again, using the AppStore on your watch:

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copied from: Redownload apps and games from Apple - Apple Support