  In this work, we examine the effects of mergers on the hydrostatic mass
estimate of galaxy clusters using high-resolution Eulerian cosmological
simulations. We utilize merger trees to isolate the last merger for each
cluster in our sample and follow the time evolution of the hydrostatic mass
bias as the systems relax. We find that during a merger, a shock propagates
outward from the parent cluster, resulting in an overestimate in the
hydrostatic mass bias. After the merger, as a cluster relaxes, the bias in
hydrostatic mass estimate decreases but remains at a level of -5-10% with
15-20% scatter within r500. We also investigate the post-merger evolution of
the pressure support from bulk motions, a dominant cause of this residual mass
bias. At r500, the contribution from random motions peaks at 30% of the total
pressure during the merger and quickly decays to \sim 10-15% as a cluster
relaxes. Additionally, we use a measure of the random motion pressure to
correct the hydrostatic mass estimate. We discover that 4 Gyr after mergers,
the direct effects of the merger event on the hydrostatic mass bias have become
negligible. Thereafter, the mass bias is primarily due to residual bulk motions
in the gas which are not accounted for in the hydrostatic equilibrium equation.
We present a hydrostatic mass bias correction method that can recover the
unbiased cluster mass for relaxed clusters with 9% scatter at r500 and 11%
scatter in the outskirts, within r200.
