ように頼んで

ask someone to

→ よう
phrase Rare #30,609
ask someone to Used to ask or tell someone to request that another person do something. The verb before ように describes the requested action; 頼んで is the て-form of 頼む, often followed by ください or another request expression.
JA: 彼に駅まで送ってくれるように頼んで。
EN: Ask him to take me to the station.

急ぐように頼んで

Could you ask them to hurry?

— ラスト、コーション (2007)

とにかく彼が戻ったらすぐに電話するように頼んでください

Anyway, please ask him to call me as soon as he gets back.

— バジュランギおじさんと、小さな迷子 (2015)

兄に乗せていってもらえるように頼んでみます

I’ll ask my older brother if he can give me a ride.

彼にもう少しいるように頼んでごらん

Try asking him to stay a little longer.