  We consider the capability of a future high energy $e^+ e^-$ collider to
search for the $Z^\prime$ bosons associated with a $U(1)^\prime$ gauge
extension of the Standard Model. Even for $Z^\prime$ masses well above the
center of mass energy of the collider, the rates of production of $e^+ e^-$,
$\mu^+ \mu^-$, unflavored jets, and $b$-tagged jets can reveal the presence of
virtual $Z^\prime$ exchange. We consider collider configurations with
center-of-mass energy 200, 300, and 500 GeV, and show how various classes of
$Z^\prime$ model-lines can be probed with $100~{\rm fb}^{-1}$ of integrated
luminosity. We find that for order one couplings, $Z^\prime$ masses on the
order of several TeV can be discovered, depending on the collider energy. Our
results suggest that a 200 GeV collision energy is unlikely to discover any of
the $Z^\prime$ models we consider that would not have already been visible in
late stages of LHC running, but could still help refine understanding of the
couplings and distinguish between different models. For $e^+ e^-$ collision
energies of 300 GeV, parameter space beyond the reach of the LHC becomes
accessible.
