  We use K-band spectroscopic data from the Multi-Object Spectroscopic Emission
Line (MOSEL) survey to analyze the kinematic properties of galaxies at z>3. Our
sample consists of 34 galaxies at 3.0<zspec<3.8 between 9.0<log(M_star)<11.0.
We find that galaxies with log(M_star) > 10.2 at z > 3 have 56 +/- 21 km/s
lower integrated velocity dispersion compared to galaxies at z ~ 2 of similar
stellar mass. Massive galaxies at z > 3 have either a flat or declining star
formation history (SFH), whereas similar stellar mass galaxies at z~2.0 exhibit
a slight peak in the past 500 Myrs. Comparing with the IllustrisTNG
cosmological simulation, we find that (i) the dynamical mass of massive
galaxies in simulations (log(M_star) > 10.0) increases by ~0.1 dex at a fixed
stellar mass between z=2.0-3.0, and (ii) dynamical mass growth is coupled with
a rapid rise in the ex-situ stellar mass fraction (stars accreted from other
galaxies) for massive galaxies at z < 3.5. We speculate that the rising
contribution of ex-situ stellar mass to the total stellar mass growth of
massive galaxies is driving the higher integrated velocity dispersion and
rising SFHs of massive galaxies at z~2.0 compared to galaxies of similar
stellar masses at z > 3.
