  In this paper, we present pressure dependent structural parameters and
electronic structure of ThFeAsN superconductor. There are no anomalies in the
structural parameters as well as elastic constants with hydrostatic pressure
which is consistent with the experiments. We study the electronic structure of
this compound at different external pressures in terms of density of states,
band structure and Fermi surface. Density of states at the Fermi level, coming
from Fe-d orbitals follows the same trend as that of the superconducting
transition temperature (T$_c$) as a function of hydrostatic pressure. We also
observe a pressure induced orbital selective Lifshitz transition in ThFeAsN
compound which is quite different from the Lifshitz transitions observed in the
other families of Fe-based superconductors. Fermi surfaces of ThFeAsN specially
hole like Fermi surfaces at $\Gamma$ point are altered significantly with
pressure. This modification of Fermi surface topology with pressure seems to
play the major role in the reduction of T$_c$ with pressure in ThFeAsN
superconductor. Spin-orbit coupling does not affect the Lifshitz transition but
it modifies the energy ordering of bands near $\Gamma$ point at higher
pressure.
