To have influence or connections; to have clout or pull in a particular circle, so that one can get favors or preferential treatment.
彼は業界で顔が利くので、イベントの出演を頼みやすい。
He has clout in the industry, so it's easy to ask him to get someone to appear at events.
友達の顔が利くからといって、無理なお願いは避けた方がいい。
Even if your friend has influence, it's better to avoid asking unreasonable favors.
この店は常連客の顔が利くので、予約が取りやすいことがある。
This restaurant sometimes accommodates reservations easily because regular customers have pull there.