  The present paper reports a study on the cosmological consequences arising
from reconstructing $f(T)$ gravity through new holographic-polytropic dark
energy. We assume two approaches, namely a particular form of Hubble parameter
$H$ and a solution for $f(T)$. We obtain the deceleration parameter, effective
equation of state as well as torsion equation of state parameters from total
density and pressure in both cases. It is interesting to mention here that the
deceleration and torsion equation of state represent transition from
deceleration to acceleration phase. We study the statefinder parameters under
both approaches which result that statefinder trajectories are found to attain
$\Lambda$CDM point. The comparison with observational data represents
consistent results. Also, we discuss the stability of reconstructed models
through squared speed of sound which represents stability in late times.
