  In this work, the large-scale shell-model calculations for $\beta$-decay
properties have been done. The $\beta$-delayed $\gamma$-ray spectroscopy has
been performed recently at ILL, Grenoble [M. Si \textit{et al.}, Phys. Rev. C
{\bf 106}, 014302 (2022)] to study $\beta$-decay properties corresponding to
$^{137}$Te (($7/2^-))$ $\rightarrow$ $^{137}$I ($J_f$) transitions. We have
done a systematic shell-model study for nuclear structure properties and
compared the obtained results with the experimental data. Finally, the
$\beta$-decay properties such as the $\log ft$ values and average shape factors
have been reported. This is the first theoretical calculation for the $\log ft$
values corresponding to these new experimental data. In addition, we have also
reported calculated $\log ft$ results for $^{135}$Te (($7/2^-))$ $\rightarrow$
$^{135}$I ($J_f$) transitions.
