  In this paper, we investigate the discovery prospect of simplified fermionic
dark sectors models through Higgs precision measurements at $e^+e^-$ colliders
and direct searches at hadron colliders. These models extend the Standard Model
with two Majorana or Dirac fermions that are singlets, doublets or triplets
under the weak SU(2) group. For all models, we consider two scenarios where the
lightest new fermion is either stable, or where it decays into other visible
final states. For the Higgs precision observables we primarily focus on
$\sigma(e^+e^-\to ZH)$, which can deviate from the Standard Model through
one-loop corrections involving the new fermions. Deviations of 0.5\% or more,
which could be observable at future $e^+e^-$ colliders, are found for TeV-scale
dark sector masses. By combining the constraints from the oblique parameters,
$\text{Br}(H\to\gamma\gamma)$, and direct production of the new fermions at the
LHC, a comprehensive understanding of the discovery potential of these models
can be achieved. In both scenarios, there exist some parameter regions where
the Higgs precision measurements can provide complementary information to
direct LHC searches.
