  We investigate the contribution of the beamed jet component to the high
energy emission in young and compact extragalactic radio sources, focusing for
the first time on the gamma-ray band. We derive predictions on the gamma-ray
luminosities associated with the relativistic jet assuming a leptonic radiative
model. The high energy emission is produced via Compton scattering by the
relativistic electrons in a spherical region at the considered scales
($\lesssim$10 kpc). Simulations show a wide range of gamma-ray luminosities,
with intensities up to $\sim10^{46}-10^{48}$ erg s$^{-1}$ depending on the
assumed jet parameters. We find a highly linear relation between the simulated
X-ray and gamma-ray luminosities that can be used to select candidates for a
gamma-ray detection. We compare the simulated luminosity distributions in the
radio, X-ray and gamma-ray regimes with observations for the largest sample of
X-ray detected young radio quasars. Our analysis of $\sim$4-year Fermi Large
Area Telescope (LAT) data does not give any statistically significant
detection. However, the majority of the model-predicted gamma-ray fluxes for
the sample are near or below the current Fermi-LAT flux threshold and
compatible with the derived upper limits. Our study gives constraints on the
minimum jet power ($L_{jet,kin}/L_{disk}>0.01$), on a potential jet
contribution to the X-ray emission in the most compact sources ($\lesssim1$
kpc) and on the particles to magnetic field energy density ratio in broad
agreement with equipartition assumption.
