  The quantum spin liquid states as a natural ground state of the Kitaev model
has led to a quest for new materials candidates hosting Kitaev physics. Yet,
there are very few material candidates in this category. Using a combination of
$ab$ $initio$ and model Hamiltonian methods, we propose that Ruddlesden-Popper
compound Sr$_4$RhO$_6$ belongs to this category. With a tight-binding model and
exact diagonalization approach, we show that despite substantial trigonal-like
distortion, the electronic and magnetic properties of Sr$_4$RhO$_6$ can be well
described in terms of pseudo-spin = 1/2 states. Magnetic interactions among
pseudo-spins, estimated using the second-order perturbation method are highly
bond-dependent anisotropic in nature with two particularly noticeable features,
antiferromagnetic Kitaev and Dzyaloshinskii-Moriya interactions. The gaped
spin-wave spectra of Sr$_4$RhO$_6$ obtained with linear spin-wave theory is
consistent with the underlying magnetic frustration. Additional analysis of the
role of individual or a particular combination of magnetic interactions reveals
that the spin-wave spectra of Sr$_4$RhO$_6$ is a combined effect of the highly
anisotropic interactions and a relatively simpler minimal model may not be
plausible in the current case. The crucial insights about coupling between the
local structural features and magnetic properties of Sr$_4$RhO$_6$ obtained in
this study may be helpful for future studies belonging to this class.
