  The self-couplings of the electroweak gauge bosons are completely specified
by the non-Abelian gauge nature of the Standard Model (SM). The direct study of
these couplings provides a significant opportunity to test the validity of the
SM and the existence of new physics beyond the SM up to the high energy scale.
For this reason, we investigate the potential of the processes
$\gamma\gamma\rightarrow ZZ$, $e^{-}\gamma\rightarrow e^{-}\gamma^{*}\gamma
\rightarrow e^{-}Z\, Z$ and $e^{+}e^{-} \rightarrow e^{+}\gamma^{*} \gamma^{*}
e^{-} \rightarrow e^{+}\, Z\, Z\, e^{-}$ to examine the anomalous quartic
couplings of $ZZ\gamma\gamma$ vertex at the Compact Linear Collider (CLIC) with
center-of-mass energy $3$ TeV. We calculate $95\%$ confidence level
sensitivities on the dimension-8 parameters with various values of the
integrated luminosity. We show that the best bounds on the anomalous
$\frac{f_{M2}}{\Lambda^{4}}$, $\frac{f_{M3}}{\Lambda^{4}}$,
$\frac{f_{T0}}{\Lambda^4}$ and $\frac{f_{T9}}{\Lambda^4}$ couplings arise from
$\gamma\gamma\rightarrow ZZ$ process among those three processes at
center-of-mass energy of 3 TeV and integrated luminosity of $L_{int}=2000$
fb$^{-1}$ are found to be $[-3.30;3.30]\times 10 ^{-3}$ TeV$^{-4}$,
$[-1.20;1.20]\times 10 ^{-2}$ TeV$^{-4}$, $[-3.40;3.40]\times 10 ^{-3}$
TeV$^{-4}$ and $[-1.80;1.80]\times 10 ^{-3}$ TeV$^{-4}$, respectively.
