  HESS J1813$-$178 is a very-high-energy $\gamma$-ray source spatially
coincident with the young and energetic pulsar PSR J1813$-$1749 and thought to
be associated with its pulsar wind nebula (PWN). Recently, evidence for
extended high-energy emission in the vicinity of the pulsar has been revealed
in the Fermi Large Area Telescope (LAT) data. This motivates revisiting the
HESS J1813$-$178 region, taking advantage of improved analysis methods and an
extended data set. Using data taken by the High Energy Stereoscopic System
(H.E.S.S.) experiment and the Fermi-LAT, we aim to describe the $\gamma$-ray
emission in the region with a consistent model, to provide insights into its
origin. We performed a likelihood-based analysis on 32 hours of H.E.S.S. data
and 12 years of Fermi-LAT data and fit a spectro-morphological model to the
combined datasets. These results allowed us to develop a physical model for the
origin of the observed $\gamma$-ray emission in the region. In addition to the
compact very-high-energy $\gamma$-ray emission centered on the pulsar, we find
a significant yet previously undetected component along the Galactic plane.
With Fermi-LAT data, we confirm extended high-energy emission consistent with
the position and elongation of the extended emission observed with H.E.S.S.
These results establish a consistent description of the emission in the region
from GeV energies to several tens of TeV. This study suggests that HESS
J1813$-$178 is associated with a $\gamma$-ray PWN powered by PSR J1813$-$1749.
A possible origin of the extended emission component is inverse Compton
emission from electrons and positrons that have escaped the confines of the
pulsar and form a halo around the PWN.
