  We investigate the quantum interference induced shifts between energetically
close states in highly charged ions, with the energy structure being observed
by laser spectroscopy. In this work, we focus on hyperfine states of
lithiumlike heavy-$Z$ isotopes and quantify how much quantum interference
changes the observed transition frequencies. The process of photon excitation
and subsequent photon decay for the transition $2s\rightarrow2p\rightarrow2s$
is implemented with fully relativistic and full-multipole frameworks, which are
relevant for such relativistic atomic systems. We consider the isotopes
$^{207}$Pb$^{79+}$ and $^{209}$Bi$^{80+}$ due to experimental interest, as well
as other examples of isotopes with lower $Z$, namely $^{141}$Pr$^{56+}$ and
$^{165}$Ho$^{64+}$. We conclude that quantum interference can induce shifts up
to 11% of the linewidth in the measurable resonances of the considered
isotopes, if interference between resonances is neglected. The inclusion of
relativity decreases the cross section by 35%, mainly due to the complete
retardation form of the electric dipole multipole. However, the contribution of
the next higher multipoles (e.g. magnetic quadrupole) to the cross section is
negligible. This makes the contribution of relativity and higher-order
multipoles to the quantum interference induced shifts a minor effect, even for
heavy-$Z$ elements.
