  Quasi-one-dimensional magnet NiCl$_2\cdot$4SC(NH$_2$)$_2$, usually
abbreviated as DTN, does not order at zero field down to $T=0$: due to the
strong single-ion anisotropy of the "easy plane" type acting on $S=1$ Ni$^{2+}$
ions, the $S_z=0$ ground state is separated from $S_z=\pm 1$ excitations by an
energy gap. Once the magnetic field is applied along the main anisotropy axis,
the gap closes at $B_{c1}=2.18$ T and the field-induced antiferromagnetic order
arises. The low-energy excitations spectrum of this field-induced ordered state
includes two branches of excitations, one of them have to be a gapless
Goldstone mode. Recent studies of excitations spectrum in a field-induced
ordered state of DTN (T.Soldatov et.al, Phys.Rev.B 101, 104410 (2020)) have
revealed that Goldstone mode became gapped as magnetic field deviates from the
main symmetry axis. This paper proposes simple description of antiferromagnetic
resonance modes of quasi-one-dimensional quantum $S=1$ magnet with strong
single-ion anisotropy. The approach used is based on a combination of the
strong coupling model for the anisotropic spin chain with the conventional
mean-field model of antiferromagnetic resonance. The resulting model fits to
the known experimental results without additional tuning parameters.
