Although gravity is not a Y-M field, you can formulate it as a gauge theory of the local Poincare group. The "gauge potentials" for translations are vierbeins (tetrads) and spin connections correspond to local Lorentz transformations.
We used this trick when working with supergravity. The regular Y-M fields were just the components of gravitational fields in compactified dimensions, a la Kaluza-Klein.