  We have calculated static and dynamic electric dipole (E1) polarizabilities
($\alpha_F$) of the hyperfine levels of the clock transition precisely in
$^{133}$Cs. The scalar, vector, and tensor components of $\alpha_F$ are
estimated by expressing as sum of valence, core, core-core, core-valence, and
valence-core contributions that are arising from the virtual and core
intermediate states. The dominant valence contributions are estimated by
combining a large number of matrix elements of the E1 and magnetic dipole
hyperfine interaction operators from the relativistic coupled-cluster method
and measurements. For an insightful understanding of their accurate
determination, we explicitly give intermediate contributions in different forms
to the above quantities. Very good agreement of the static values for the
scalar and tensor components with their experimental results suggest that our
estimated dynamic $\alpha_F$ values can be used reliably to estimate the Stark
shifts while conducting high-precision measurements at the respective laser
frequency using the clock states of $^{133}$Cs.
