  The present work is based on the idea of an interacting framework of new
holographic dark energy with cold dark matter in the background of $f(T)$
gravity. Here, we have considered the flat modified Friedmann universe for
$f(T)$ gravity which is filled with new Holographic dark energy and dark
matter. We have derived some cosmological parameters like Deceleration
parameter, EoS parameter, State-finder parameters, Cosmographic parameters,
{\it Om} parameter and graphically investigated the nature of these parameters
for the above mentioned interacting scenario. The results are found to be
consistent with the accelerating universe. Also we have graphically
investigated the trajectories in $\omega $--$ \omega'$ plane for different
values of the interacting parameter and explored the freezing region and
thawing region in $\omega $--$ \omega'$ plane. Finally, we have analyzed the
stability of this model.
