To Entrust Something
To Delegate Something, To Leave Something To
transitive verb, godan verb
The meaning of this word is the same as 任せる. Both words are pretty common, but 任す is slightly less common than 任せる.
Here's the mnemonic again, just in case you need a refresher:
If you pass a duty on to someone, that means you're going to entrust something to that person, or you're going to delegate something. In other words, you're going to leave something to them, so that they do it for you.
This uses the same reading you learned with 任せる.
この店のことは全て君の判断に任すよ。
I'll leave everything about this store to your judgment.
大きな仕事を任されて、うれしいけど少し不安でもある。
I'm happy to be entrusted with a big job, but I'm also a little nervous.
今回、プロジェクトマネージャーを任されることになった田中です。よろしくお願いします。
I'm Tanaka and I've been assigned as project manager. I look forward to working with you all.