In this article, the perfect fluid is introduced for plane symmetric space–time in the framework of teleparallel gravity using hybrid expansion law (HEL). The behaviour of accelerating Universe is discussed by considering the depiction model of $f (T )$ gravity, i.e. $f (T ) = T ^{\eta}$. The geometrical and physical parameters of the model are studied. An effective equation of state (EoS) has been investigated in the cosmological evolution with perfect fluid. The basic equations of thermodynamics have been deduced and the thermodynamical aspects of the model have been discussed. Thermodynamic temperature and entropy density of the model are also obtained. The statefinder parameters and jerk parameter analysis are discussed for our obtained model to distinguish our model from other dark energy models.