  The two-dimensional triangular-lattice antiferromagnet (TLAF) is a textbook
example of frustrated magnetic systems. Despite its simplicity, the TLAF model
exhibits a highly rich and complex magnetic phase diagram, featuring numerous
distinct ground states that can be stabilized through frustrated next-nearest
neighbor couplings or anisotropy. In this paper, we report low-temperature
magnetic properties of the TLAF material CsCeSe$_2$. The inelastic neutron
scattering (INS) together with specific heat measurements and density
functional theory calculations of crystalline electric field suggest that the
ground state of Ce ions is a Kramers doublet with strong easy-plane anisotropy.
Elastic neutron scattering measurements demonstrate the presence of stripe-$yz$
magnetic order that develops below $T_{\rm N} = 0.35$ K, with the zero-field
ordered moment of $m_{\rm Ce} \approx 0.65~\mu_{\rm B}$. Application of
magnetic field first increases the ordering temperature by about 20% at the
intermediate field region and eventually suppresses the stripe order in favor
of the field-polarized ferromagnetic state via a continuous quantum phase
transition (QPT). The field-induced response demonstrates sizable anisotropy
for different in-plane directions, $\mathbf{B}\parallel{}\mathbf{a}$ and
$\mathbf{B}\perp{}\mathbf{a}$, which indicates the presence of bond-dependent
coupling in the spin Hamiltonian. We further show theoretically that the
presence of anisotropic bond-dependent interactions can change the universality
class of QPT for $\mathbf{B}\parallel{}\mathbf{a}$ and
$\mathbf{B}\perp{}\mathbf{a}$.
