  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 exhibits the usual
thermal history, namely the successive sequence of radiation, dark matter and
dark energy epochs, before resulting in a complete dark energy domination in
the far future. It is shown the evolution of the 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.
