The phrase "to approach a publisher" means to contact or communicate with a company that publishes books or other written works to possibly pitch or present your own work for consideration to be published by them. Full definition
If this is the case, forget the agent and approach the publisher directly. (thecreativepenn.com)
It is also worth noting that even though you have published a successful book independently, in many ways when approaching a publisher you need to start from scratch and produce a manuscript. (readersfavorite.com)
On the other side of the spectrum, approaching publishers for publishing your first poetry books is a huge mistake. (changingthescript.com)