The act of one who chases another; a pursuit.

A hunt.

A children's game where one player chases another.

To pursue.

To consume another beverage immediately after drinking hard liquor, typically something better tasting or less harsh such as soda or beer; to use a drink as a chaser

“I need something to chase this shot with.”

To attempt to win by scoring the required number of runs in the final innings.

“Australia will be chasing 217 for victory on the final day.”