I want to restain the vanity in my bathroom the same color or maybe slightly darker. Will I need a primer before restaining the wood finish?
A primer isn't needed. Actually this will interfere with the stain color. There are a couple of different ways to this; strip off all old finish and stain for stain over the existing finish. The one that best suits your situation depends on the condition of the cabinet.
Check out these links for more info and instructions;
<a href="https://www.house-painting-info.com/cabinet-refinishing.html">Cabinet Refinishing</a> (lots of articles that will help) and <a href="https://www.house-painting-info.com/restain-cabinets.html">Restain Cabinets for a New Look</a>.