go after
verb- To pursue in attempt to catch another. · The downed officer couldn't go after the criminal.
- To pursue an object or a goal. · In Little League, usually everyone goes after the ball.· Inspired, the scientist went right after the new idea.
From the library
“I will just go after him and see what he does with himself.” With those words he took his hat and started off down the street.
Alice did not quite like the look of the creature, but on the whole she thought it would be quite as safe to stay with it as to go after that savage Queen: so she waited.
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