The present paper reports a study on the cosmological consequences arising from reconstructing $f\left(T\right)$ gravity through new holographic polytropic dark energy. We assume two approaches, namely, a particular form of Hubble parameter $H$ and a solution for $f\left(T\right)$. We obtain the deceleration parameter and 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 in the fact that statefinder trajectories are found to attain ΛCDM 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.