Meaning: to quickly consume the rest of a drink
Examples:
She drank up what was left of her beer and left in a hurry.
He told me to drink up because there wouldn’t be more water, we are going to the desert today.
To get out
Meaning: to become known, to become public knowledge Examples: I don't want it to get out that I am leaving. Please don't tell anyone. If this bad news gets out, people will panic and try to run away.