“勾结着”常见的英文表达可以是 “in collusion with” （强调秘密、不正当的勾结行为，常用于正式语境）或 “conspiring with” （侧重于有预谋、共同策划的勾结，语气稍重） 。
In collusion with：
例句：The official was found to be in collusion with the criminal gang.（发现这位官员与犯罪团伙勾结。）
Conspiring with：
例句：They were conspiring with each other to cheat in the election.（他们互相勾结，企图在选举中作弊 。）