  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
$[P_0,c_{500},\alpha,\beta,\gamma]=[5.048,1.217,1.192,5.490,0.433]$ 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. $\Omega_\text{m}=0.3$, $\sigma_8 = 0.8$),
and is broadly consistent with recent Planck results without requiring
additional bias corrections.
