  Using density functional theory (DFT) and linear response approaches, we
compute the on-site Hubbard interaction $U$ of elemental Terbium (Tb) metal in
the pressure range $\sim 0-65$ GPa. The resulting first-principles $U$ values
with experimental crystal structures enable us to examine the magnetic
properties of Tb using a self-consistent DFT+U method. The lowest-energy
magnetic states in our calculations for different high-pressure Tb phases --
including hcp, $\alpha$-Sm, and dhcp -- are found to be compatible with the
corresponding magnetic ordering vectors reported in experiments. The result
shows that the inclusion of Hubbard $U$ substantially improves the accuracy and
efficiency in modeling correlated rare-earth materials. Our study also provides
the necessary $U$ information for other quantum many-body techniques to study
Tb under extreme pressure conditions.
