  The two-dimensional $q$-state clock models exhibit the
Berezinskii-Kosterlitz-Thouless (BKT) transition for $q\geq5$ since they are a
subset of the isotropic XY model. We examine the $6$-state clock model with an
anisotropic deformation. Selecting the $6$-state Potts model as a source of the
deformation, the model naturally violates the discrete rotational symmetry of
the clock model. We introduce the anisotropic deformation parameter $\alpha$ in
the clock model interpolating the clock ($\alpha = 1$) and the Potts ($\alpha =
0$) models. We employ the corner transfer matrix renormalization group method
to analyze the phase transitions on the square lattice in the thermodynamic
limit. Three different phases and phase transitions are identified. The phase
diagram is constructed, and we determine a tricritical point at $\alpha_{\rm c}
= 0.21405(4)$ and $T_{\rm c} = 0.834017(5)$. Analyzing the latent heat and the
entanglement entropy in the vicinity of the $T_{\rm c}(\alpha_{\rm c})$, we
observe a single discontinuous phase transition and two BKT phase transitions
meeting in the tricritical point. The tricritical point exhibits a phase
transition of the second order with the critical exponents $\beta \approx 1/10$
and $\delta \approx 14$. We conjecture that an infinitesimal surrounding of the
tricritical point consists of the three fundamental phase transitions, in which
the first and the BKT orders gradually weaken into the second-order tricritical
point.
