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Spontaneous breaking of the $SU(2)_{L}\times U(1)_{Y}$ electroweak symmetryof the Standard Model (SM) sets the constraints on triple gauge couplings andquartic gauge couplings. Therefore, the measurement of multiboson production in$e^{-} e^{+}$ collisions allows us to directly examine the SM predictions andperform indirect investigations of new physics beyond the SM. In this paper, weconcentrate the process $e^{-} e^{+} \to e^{-} Z\gamma e^{+}$ with $Z$ bosondecaying to neutrinos to investigate the anomalous quartic gauge couplingsusing 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 uncertaintiesof $3, 5 \%$ at $95\%$ Confidence Level for the CLIC with $\sqrt{s}=3$ TeV. Ourresults show that the sensitivities on some anomalous couplings withoutsystematic errors are up to two orders of magnitude better than the currentexperimental limits. Considering a realistic systematic uncertainty such as $5\%$ from possible experimental sources, the sensitivity of all anomalousquartic couplings gets worse by about $10\%$ compared to those withoutsystematic uncertainty for the CLIC.

Search for the anomalous quartic gauge couplings through $Z\gamma$ production at $e^{-} e^{+}$ colliders