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In this work, we study the spectral statistics for Anderson model on $\ell^2(\mathbb{N})$ with decaying randomness whose single site distribution has unbounded support. Here we consider the operator $H^\omega$ given by $(H^\omega u)_n=u_{n+1}+u_{n-1}+a_n\omega_n u_n$, $a_n\sim n^{-\alpha}$ and $\{\omega_n\}$ are real i.i.d random variables following symmetric distribution $\mu$ with fat tail, i.e $\mu((-R,R)^c) \frac{1}{2}$, we are able to show that the eigenvalue process in $(-2,2)$ is the clock process.

Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential