  Spontaneous breaking of the $SU(2)_{L}\times U(1)_{Y}$ electroweak symmetry
of the Standard Model (SM) sets the constraints on triple gauge couplings and
quartic gauge couplings. Therefore, the measurement of multiboson production in
$e^{-} e^{+}$ collisions allows us to directly examine the SM predictions and
perform indirect investigations of new physics beyond the SM. In this paper, we
concentrate the process $e^{-} e^{+} \to e^{-} Z\gamma e^{+}$ with $Z$ boson
decaying to neutrinos to investigate the anomalous quartic gauge couplings
using the effective Lagrangian approach at the Compact Linear Collider (CLIC).
We obtain the sensitivities on the anomalous $ f_ {Ti}/\Lambda^4$
($i=0,2,5,6,7,8,9$) couplings taking into account the systematic uncertainties
of $3, 5 \%$ at $95\%$ Confidence Level for the CLIC with $\sqrt{s}=3$ TeV. Our
results show that the sensitivities on some anomalous couplings without
systematic errors are up to two orders of magnitude better than the current
experimental limits. Considering a realistic systematic uncertainty such as $5
\%$ from possible experimental sources, the sensitivity of all anomalous
quartic couplings gets worse by about $10\%$ compared to those without
systematic uncertainty for the CLIC.
