Fetching details from the dictionary...

to leave (a matter, decision, etc. to someone); to entrust (to someone); to entrust (someone) with
to leave (to chance, one's imagination, etc.); to let (take its own course); to let (happen); to give (oneself to something)
to use (money, strength, spare time, etc.) to the full; to use freely; to use without reserve
この仕事は君に任せるからね。
I'm leaving this job to you.
結果は運に任せるしかない。
We have no choice but to leave the outcome to luck.
今回のプロジェクトは部下に全て任せた。
I left this entire project to my subordinates.