仲介する｜intermediate ((between)); mediate ((between))
through the intermediation [mediation] of...
The United States acted as an intermediary in ceasefire talks between the two countries.
He offered to mediate between the two families to help them mend their differences.
仲介者｜an intermediary, a go-between; 〔調停者〕a mediator; 〔周旋人〕an agent, a broker
仲介手数料｜a brokerage fee
仲介貿易｜trade carried on through an agent; agency business