The issue isn't whether publishers promote new authors or not, it's to do with investment.
The more a publisher invests in a book, the more they are going to do to push it regardless of who wrote it.
Established, successful authors tend to be paid bigger advances and get bigger promotional budgets, while new authors tend to be paid smaller advances with matching marketing efforts.
Generally speaking, any authors who are paid small advances will find those matched by smaller marketing spends; any authors who are paid huge advances will get matching huge marketing efforts.
It really helps if you have a good agent here, as they'll work to get a marketing commitment added to your contract, and will then ensure your publisher adheres to that contract.