  The aim of this paper is to analyze the cosmological evolution of holographic
dark energy in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the
Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively).
We reconstruct $f(\mathcal{G},T)$ model through correspondence scheme using
power-law form of the scale factor. The qualitative analysis of the derived
model is investigated with the help of evolutionary trajectories of equation of
state, deceleration as well as state-finder diagnostic parameters and
$\omega_{_{\mathcal{G}T}}-{\omega}'_{_{\mathcal{G}T}}$ cosmological phase
plane. It is found that the equation of state parameter represents phantom
epoch of the Universe whereas the deceleration parameter illustrates the
accelerated phase. The state-finder plane corresponds to Chaplygin gas model
while the freezing region is attained in
$\omega_{_{\mathcal{G}T}}-{\omega}'_{_{\mathcal{G}T}}$ plane.
