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The Navier-Stokes equations play an essential role in many practical and engineering design applications. Hence the efficient and high fidelity solution of the problem is one of the foci of research in scientific computing. In this work, we generalize the pressure convection-diffusion (PCD) preconditioner to the hybridized discontinuous Galerkin (HDG) discretization of Rhebergen and Wells. We will discuss the discretization and why we prefer it over methods and then we will introduce the idea behind the preconditioner. Afterward, we will talk about the challenges specific to the HDG discretization. For example, while this discretization lends itself to static condensation through which we can obtain significantly smaller linear systems of equations, it comes at the cost of difficulty in designing preconditioners. On the other hand, if we do not use static condensation it is straightforward to employ the PCD preconditioner; however, we have to solve a larger linear system of equations. Finally, we are going to compare the results (static condensation vs. full) in terms of efficiency.