We report on a possible association of the recently discovered very high-energy $\gamma$-ray source HESS J1825–137 with the pulsar wind nebula (commonly referred to as G 18.0–0.7) of the $2.1\times 10^{4}$ year old Vela-like pulsar PSR B1823–13. HESS J1825–137 was detected with a significance of 8.1 $\sigma$ in the Galactic Plane survey conducted with the H.E.S.S. instrument in 2004. The centroid position of HESS J1825–137 is offset by 11\arcmin south of the pulsar position. \emph{XMM-Newton} observations have revealed X-ray synchrotron emission of an asymmetric pulsar wind nebula extending to the south of the pulsar. We argue that the observed morphology and TeV spectral index suggest that HESS J1825–137 and G 18.0–0.7 may be associated: the lifetime of TeV emitting electrons is expected to be longer compared to the {\it XMM-Newton} X-ray emitting electrons, resulting in electrons from earlier epochs (when the spin-down power was larger) contributing to the present TeV flux. These electrons are expected to be synchrotron cooled, which explains the observed photon index of $\sim 2.4$, and the longer lifetime of TeV emitting electrons naturally explains why the TeV nebula is larger than the X-ray size. Finally, supernova remnant expansion into an inhomogeneous medium is expected to create reverse shocks interacting at different times with the pulsar wind nebula, resulting in the offset X-ray and TeV $\gamma$-ray morphology.
