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We demonstrate that several metastable excited states in Hf$~$II, Hf$~$IV andW$~$VI ions may be good clock states since they are sufficiently long-livingand are not sensitive to the perturbations. Cooling E1 transitions areavailable. Energy levels, Land\'{e} $g$-factors, transition amplitudes forelectric 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 ofrelativistic many-body calculations including the configuration interaction(CI), linearized coupled-cluster single-doubles (SD) and many-body perturbationtheory (CI+SD), and also the configuration interaction with perturbation theory(CIPT). Scalar polarizabilities of the ground states and the clock states havebeen calculated to determine the black body radiation (BBR) shifts. We havefound that the relative BBR shifts for these transitions range between10$^{-16}$ $-$ 10$^{-18}$. A linear combination of two clock transitionfrequencies allows one to further suppress BBR. Several $5d$ - $6s$single-electron clock transitions ensure high sensitivity of the transitionfrequencies to the variation of the fine structure constant $\alpha$ and may beused to search for dark matter producing this variation of $\alpha$. Theenhancement coefficient for $\alpha$ variation reaches $K=8.3$. Six stableisotopes of Hf and 5 stable isotopes in W allow one to make King plots andsearch for new interactions mediated by scalar particles or other mechanisms.

Atomic clocks highly sensitive to the variation of the fine structure constant based on Hf II, Hf IV, and W VI ions