  We demonstrate that several metastable excited states in Hf$~$II, Hf$~$IV and
W$~$VI ions may be good clock states since they are sufficiently long-living
and are not sensitive to the perturbations. Cooling E1 transitions are
available. Energy levels, Land\'{e} $g$-factors, transition amplitudes for
electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1)
transitions, lifetimes, and electric quadrupole moments for Hf$~$II, Hf$~$IV,
and W$~$VI ions are investigated using a combination of several methods of
relativistic many-body calculations including the configuration interaction
(CI), linearized coupled-cluster single-doubles (SD) and many-body perturbation
theory (CI+SD), and also the configuration interaction with perturbation theory
(CIPT). Scalar polarizabilities of the ground states and the clock states have
been calculated to determine the black body radiation (BBR) shifts. We have
found that the relative BBR shifts for these transitions range between
10$^{-16}$ $-$ 10$^{-18}$. A linear combination of two clock transition
frequencies allows one to further suppress BBR. Several $5d$ - $6s$
single-electron clock transitions ensure high sensitivity of the transition
frequencies to the variation of the fine structure constant $\alpha$ and may be
used to search for dark matter producing this variation of $\alpha$. The
enhancement coefficient for $\alpha$ variation reaches $K=8.3$. Six stable
isotopes of Hf and 5 stable isotopes in W allow one to make King plots and
search for new interactions mediated by scalar particles or other mechanisms.
