chase
noun
tʃeɪs 
tʃeɪs running/driving after
1 [countable] (often used with the) an act of running or driving after somebody/something in order to catch themThe thieves were caught by police after a short chase.a high-speed car chaseWe lost him in the narrow streets and had to give up the chase (= stop chasing him).to take up the chase (= start chasing somebody)The chase is on!for success/money/work
2 [singular] a process of trying hard to get somethingThree teams are involved in the chase for the championship.the title chasein sport
3 the chase [singular] hunting animals as a sportShe enjoyed the thrill of the chase.4 [countable] = steeplechase see also wild goose chaseIdioms
cut to the chase
(informal) to stop wasting time and start talking about the most important thingRight, let's cut to the chase. How much is it going to cost?give chase
to run after somebody/something in order to catch them
We gave chase along the footpath.