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We present an updated model for the average cluster pressure profile, adjusted for hydrostatic mass bias by combining results from X-ray observations with cosmological simulations. Our model estimates this bias by fitting a power-law to the relation between the "true" halo mass and X-ray cluster mass in hydrodynamic simulations (IllustrisTNG, BAHAMAS, and MACSIS). As an example application, we consider the REXCESS X-ray cluster sample and the Universal Pressure Profile (UPP) derived from scaled and stacked pressure profiles. We find adjusted masses, $M_\mathrm{500c},$ that are $\lesssim$15% higher and scaled pressures $P/P_\mathrm{500c}$ that have $\lesssim$35% lower normalization than previously inferred. Our Debiased Pressure Profile (DPP) is well-fit by a Generalized Navarro-Frenk-White (GNFW) function, with parameters $[P_0,c_{500},α,β,γ]=[5.048,1.217,1.192,5.490,0.433]$ and does not require a mass-dependent correction term. When the DPP is used to model the Sunyaev-Zel'dovich (SZ) effect, we find that the integrated Compton $Y-M$ relation has only minor deviations from self-similar scaling. The thermal SZ angular power spectrum is lower in amplitude by approximately 30%, assuming nominal cosmological parameters (e.g. $Ω_\text{m}=0.3$, $σ_8 = 0.8$), and is broadly consistent with recent Planck results without requiring additional bias corrections.