The paper deals with a theoretical model for interacting Tsallis holographic dark energy ( THDE ) whose infrared ( IR ) cut-off scale is set by the Hubble length .
The interaction Q between the dark sectors ( dark energy and pressureless dark matter ) of the universe has been assumed to be non-gravitational in nature .
The functional form of Q is chosen in such a way that it reproduces well known and most used interactions as special cases .
We then study the nature of the THDE density parameter , the equation of state parameter , the deceleration parameter and the jerk parameter for this interacting THDE model .
Our study shows that the universe undergoes a smooth transition from a decelerated to an accelerated phase of expansion in the recent past and also this transition occurs within the redshift interval [ 0.637,0.962 ] .
This is well consistent with the present observations .
It is shown the evolution of the the normalized Hubble parameter for our model and compared that with the latest Hubble parameter data .
Finally , we also investigate both the stability and thermodynamic nature of this model in the present context .