decant
To carefully pour liquid from one container into another.
To decant means to carefully pour a liquid from one container into another, usually to separate the liquid from sediment or to let it breathe. When you decant grape juice from a pitcher into glasses, you're pouring it slowly and deliberately. Wine lovers decant old bottles to leave behind the gritty sediment that has settled at the bottom, or to expose young wine to air so its flavors can develop.
The word emphasizes the carefulness of the pouring. You're transferring the liquid gently and precisely, controlling the flow to avoid disturbing what you're leaving behind. Scientists decant chemicals in laboratories when they need to separate a clear liquid from particles that have sunk to the bottom of a beaker.
You might also hear people use decant more loosely to mean transferring a liquid from one container to another, like decanting shampoo from a large bottle into a smaller travel container.