There isn't a specific word for seeing the moon on a clear night. However, you can describe it in various ways:

* Observing the moon

* Gazing at the moon

* Witnessing the moon

* Enjoying the moonlit night

* Seeing a full moon (if it's a full moon)

You could also be more poetic:

* Bask in the lunar glow

* Admire the celestial orb

The best way to describe it depends on the context and the specific experience you want to convey.