In this work, we present a method for performing output-based mesh adaptation for high-order large-eddy simulations of turbulence. Instead of relying on an unsteady adjoint, which is expensive to compute and requires non-trivial regularization for chaotic flows, the proposed method is based on the idea of creating dynamic turbulence closures to first create a steady-state Reynolds-averaged (RANS) model of an unsteady system. The RANS model admits a steady adjoint solution that then drives mesh adaptation.