Coat-tails are the two long pieces at the back of a tailcoat .
PHRASE
沾…的光;靠…的提攜
If you do something on the coat-tails of someone else, you are able to do it because of the other person's success, and not because of your own efforts.
例句
They accused him of riding on the coat-tails of the president.他們指責他是沾了總統的光。