  In this paper, we have investigated the physical behavior of cosmological
models in the framework of modified Teleparallel gravity. This model is
established using a Renyi holographic ``dark energy model (RHDE) with a Hubble
cutoff. Here we have considered a homogeneous and isotropic Friedman universe
filled with perfect `fluid. The physical parameters are derived for the present
model in Compliances with 43 observational Hubble data sets (OHD). The equation
of state (EoS) parameter in terms of $H(z)$ describes a the transition of the
universe between phantom and non-phantom phases in the context of $f(T)$
gravity. Our model shows the violation of strong energy condition (SEC) and the
weak energy condition (WEC) over the accelerated phantom regime. We also
observed that these models occupy freezing regions through $\omega_{D}
-\omega_{D}^{'}$ plane. Consequently, our Renyi HDE model is supported to the
consequences of general relativity in the framework of $f(T)$ modified gravity.
