on sb's coattails

on sb's coattails (aided by association with another person)
If you achieve something on someone's coattails, you achieve it because of the other person's power or success.

to climb / hang / ride on sb's coattails (to make one's good fortune or success on the strength of someone else's; to increase one's reputation through connections to someone with a better reputation; to get a free ride to success; to try to benefit from associating with someone else who is at the top, or rise quickly to the top) — добиться (незаслуженного) успеха с помощью влиятельного лица, с помощью протекции; добиться (чего-л., успеха) по блату; пойти в гору благодаря связям, протекции; ≈ пробиться (наверх, к успеху и пр.) на чужом горбу, за чужой счет, по блату
Also ride sb's coattails and ride the coattails of sb

Example 1: I don't think she would get promoted without riding her boss's coattails. (Cambridge Dictionary of American Idioms)
Example 2: My opponent is riding the coattails of the popular governor of Massachusetts. (Cambridge Dictionary of American Idioms)

Example 3: Bill isn't very creative, so he rides on John's coattails. (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)

Example 3: A number of Republican congressmen were elected on Bush's coattails. (LDOCE)

Related vocabulary:

To sponge, mooch, free load, skate by, or do absolutely nothing but watch while somebody else does all the work and still somehow try to take at least partial credit for something you had no hand in.
coattails {pl} 1) the cloth at the back of a tailcoat that is divided into two pieces — фалды (фрака, мундира и т. п.) ==> 2) the influence or pulling power of a popular movement or person (as a political candidate) — помощь знакомого, протекция; связи в верхах; помощь влиятельного человека; помощь влиятельного родственника, блат