beat a path to (someone's) door

Translations
протоптать дорожку к (чьей-то) двери
After the success of her first book, publishers were beating a path to her door.
После успеха её первой книги издатели протаптывали дорожку к её двери.
Definitions
To frequently visit or seek out someone, often due to their popularity, influence, or the services they provide.