Vizier of Tumbling Sands

{T}: Untap another target permanent.
Cycling {1}{U} ({1}{U}, Discard this card: Draw a card.)
When you cycle Vizier of Tumbling Sands, untap target permanent.

"Time is like the Luxa River—though it flows in one direction, it can be diverted."

Commander Masters

Amonkhet Remastered

Commander 2020

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.