hunt down

Hunt down means to pursue someone or something persistently until you find or capture them.

The phrase emphasizes determined, relentless searching rather than casual looking—you hunt down a fugitive, a rare book, or the source of a mysterious smell.

Police hunted down the suspects over several months.

I finally hunted down that recipe my grandmother used to make.

The "down" suggests pursuit to completion, cornering the target until it can no longer escape.