enlist someone's help(кого-либо; I have been asked by our Moscow office to enlist your help with regard to the payment of some outstanding bills... андралекс)
get an in with(кого-то, кто может помочь решить тот или иной вопрос: The only way they'll allow us to film the play is if we get an in with the director.4uzhoj)
gain support for(to gain China's support for imposing sanctions on ... over ... – заручиться поддержкой Китая в вопросе о введении санкций в отношении ... в связи с ...Alex_Odeychuk)
shore up support(напр., с сайта IWPR – At best, simmering tensions were ignored; at worst, they were quietly exploited by politicians seeking to shore up support within their own constituencies. disk_d)
