Anomalous magnetic moment of lepton (a$\tau$) is a promising candidate to probe Beyond Standard Model(BSM) physics. Any BSM model like Supersymmetry induces correction on a$\tau$ which is proportional to the square mass of lepton. The square mass of $\tau$ is 280 times heavier than $\mu$, so it is more sensitive than $\mu$ to probe any BSM physics. The current best experimentally measured value of the anomalous magnetic moment of $\tau$ (a$_{\tau}$) is from the DELPHI experiment using 1997-2000 data collected by the DELPHI detector. In LHC $\tau$ pairs are produced in ultraperipheral (UPC) PbPb$\rightarrow$Pb($\gamma\gamma\rightarrow\tau\tau$)Pb collisions. The UPC Pb-Pb, interactions mainly happen via. photons, no hadronic interaction so the background is less. So due to the electromagnetic interaction, the LHC cross-section enjoys a Z$^4$ enhancement compared to pp. Recently CMS experiment observed PbPb$\rightarrow$Pb($\gamma\gamma\rightarrow\tau\tau$)Pb process with the one muon and three pions in the final state using 0.4nb$^{-1}$ data at $\sqrt{s}_{NN}$ = 5.02TeV. CMS experiment set limit on a$_\tau$ is ($ -8.8 $ a$_{\tau} 5.6$)$\times 10^{-2}$ at 68$\%$ CL. This study was statistically limited. We are now analyzing 1.6nb$^{-1}$ data collected by CMS to probe a$_\tau$. I am now working on $\gamma\gamma\rightarrow\tau\tau\rightarrow e^{\pm} + \mu^{\pm} + \nu^{'}s$ decay mode which combined with other decay modes will improve the statistical uncertainty. In this seminar, some preliminary studies will be shown and a detailed plan for future work will be presented.