  The delafossite family of compounds with a triangular lattice of rare earth
ions has been recently proposed as a candidate host for quantum spin liquid
(QSL) states. To realize QSLs, the crystal-electric-field (CEF) ground state of
the rare earth ions should be composed of a doublet that allows sizable quantum
tunneling, but till now the knowledge on CEF states in the delafossite
compounds is still limited. Here we employ inelastic neutron scattering (INS)
to study the CEF transitions in a powder sample of the delafossite NaErS$_2$,
where the large total angular momentum $J = 15/2$ of the Er$^{3+} $ ions and
the resulting plethora of CEF transitions enable an accurate fit of the CEF
parameters. Our study reveals nearly isotropic spins with large $J_z = \pm 1/2$
components for the Er$^{3+}$ CEF ground states, which might facilitate the
development of a QSL state. The scaling of the obtained CEF Hamiltonian to
different rare earth ions suggests that sizable $J_z = \pm 1/2$ components are
generally present in the CEF ground states, supporting the ternary sulfide
delafossites as potential QSL hosts.
