  In this work we study the hybrid kind of dark matter(DM) production mechanism
where both thermal and non-thermal contribution at two different epochs set the
DM relic abundance. This hybrid set up in turn shifts the parameter space of DM
in contrast to pure thermal DM scenario. We review such production mechanism in
the context of the $SU(2)_L$ lepton doublet dark matter ($\Psi$) augmented with
an additional singlet dark scalar ($S$). The neutral component of the dark
doublet can serve as a stable DM candidate and in pure thermal scenario, it is
under-abundant as well as excluded from direct detection constraints due to its
strong gauge interactions in the sub-TeV mass regime. However, in addition to
the thermal contribution, the late time non-thermal DM production from the
decay of the long-lived dark scalar $S$ helps to fulfill the deficit in DM
abundance. On the other hand, the strong gauge mediated direct detection
constraint can be evaded with the help of a $SU(2)_L$ triplet scalar(with
$Y=2$), resulting a pseudo-Dirac DM. To realize our proposed scenario we impose
a discrete $\mathcal{Z}_2$ symmetry under which both $\Psi$ and $S$ are odd
while rest of the fields are even. We find the lepton doublet pseudo-Dirac DM
with mass $\sim 450-1200$ GeV, compatible with the observed relic density,
direct, indirect, and existing collider search constraints.
