Shefet Monitor

Cycling {3}{G} ({3}{G}, Discard this card: Draw a card.)
When you cycle Shefet Monitor, you may search your library for a basic land card or a Desert card, put it onto the battlefield, then shuffle. (Do this before you draw.)

Amonkhet Remastered

Cycling {3}{G} ({3}{G}, Discard this card: Draw a card.)
When you cycle Shefet Monitor, you may search your library for a basic land card or a Desert card, put it onto the battlefield, then shuffle your library. (Do this before you draw.)

Amonkhet

The cycling ability and the triggered ability are separate. If the triggered ability doesn't resolve (because, for example, it has been countered, or all of its targets have become illegal), the cycling ability will still resolve, and you'll draw a card.

When you cycle this card, first the cycling ability goes on the stack, then the triggered ability goes on the stack on top of it. The triggered ability will resolve before you draw a card from the cycling ability.