  We derive the discovery potential of a leptophilic Z', and a Z' rising from a
$SU(3) \times SU(3)_L \times U(1)_N$ symmetry at the Compact Linear Collider
(CLIC), which is planned to host $e^+e^-$ collisions with 3 TeV center-of-mass
energy. We perform an optimized selection cut strategy on the transverse
momentum, pseudorapidity, and invariant mass of the dileptons in order to
enhance the collider sensitivity. We find that CLIC can potentially reach a
$5\sigma$ signal of a $1-3$~TeV leptophilic Z' with less than $1fb^{-1}$ of
integrated luminosity. As for the Z' belonging to a 3-3-1 symmetry, CLIC will
offer a complementary probe with the potential to impose $M_{Z^\prime} > 3$~TeV
with $\mathcal{L}=2fb^{-1}$.
