  The presence of multi-boson self-interactions is implied by the non-Abelian
gauge structure of the Standard Model (SM). Precise measurements of these
interactions allow not only testing the nature of the SM but also new physics
contribution arising from the beyond SM. The investigation of these
interactions can be approached in a model-independent manner using an effective
theory approach, which forms the main motivation of this study. In this paper,
we examine the anomalous neutral quartic gauge couplings through the process
$\gamma \gamma \rightarrow Z Z$ at the Compact Linear Collider (CLIC) with the
center-of-mass energy of $\sqrt{s}=3$ TeV, integrated luminosities of ${\cal
L}=5$ $\rm ab^{-1}$. The anomalous neutral quartic gauge couplings is
implemented into FeynRules to generate a UFO module inserted into Madgraph to
generate both background and signal events. These events are then passed
through Pythia 8 for parton showering and Delphes to include realistic detector
effects. We obtain that the sensitivities on the anomalous quartic neutral
gauge couplings with $95\%$ Confidence Level are given as:
$f_{T0}/\Lambda^{4}=[-1.06; 1.08]\times 10^{-3}$ ${\rm TeV^{-4}}$,
$f_{T1}/\Lambda^{4}=[-1.06; 1.08]\times 10^{-3}$ ${\rm
TeV^{-4}}$,$f_{T2}/\Lambda^{4}=[-1.06; 1.08]\times 10^{-3}$ ${\rm
TeV^{-4}}$,$f_{T0}/\Lambda^{4}=[-1.06; 1.08]\times 10^{-3}$ ${\rm TeV^{-4}}$,
$f_{T5}/\Lambda^{4}=[-4.08; 4.08]\times 10^{-4}$ ${\rm TeV^{-4}}$ and
$f_{T8}/\Lambda^{4}=[-1.10; 1.10]\times10^{-4}$ ${\rm TeV^{-4}}$. Our results
on the anomalous quartic neutral gauge couplings are set more stringent
sensitivity with respect to the recent experimental limits.
