on one's coattails
on one's coattails {adv. phr.}
Because of another's merits, success, or popularity.
Bob and Jim are best friends. When Jim was invited to join a fraternity, Bob rode in on his coattails.
Many people vote straight for all the candidates in the same political party. Most people voted for President K., so Governor B. rode in on K.'s coattails.
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Source: A Dictionary of American Idioms