  The stellar (n, $\gamma$) cross section data for the mass numbers around A
$\approx$ 160 are of key importance to nucleosynthesis in the main component of
the slow neutron capture process, which occur in the thermally pulsing
asymptotic giant branch (TP--AGB). The new measurement of (n, $\gamma$) cross
sections for $^{159}$Tb was performed using the C$_6$D$_6$ detector system at
the back streaming white neutron beam line (Back-n) of the China spallation
neutron source (CSNS) with neutron energies ranging from 1 eV to 1 MeV.
Experimental resonance capture kernels were reported up to 1.2 keV neutron
energy with this capture measurement. Maxwellian-averaged cross sections (MACS)
were derived from the measured $^{159}$Tb (n, $\gamma$) cross sections at $kT$
= 5 $\sim$ 100 keV and are in good agreement with the recommended data of
KADoNiS-v0.3 and JEFF-3.3, while KADoNiS-v1.0 and ENDF-VIII.0 significantly
overestimate the present MACS up to 40$\%$ and 20$\%$, respectively. A
sensitive test of the s-process nucleosynthesis was also performed with the
stellar evolution code MESA. Significant changes in abundances around A
$\approx$ 160 were observed between the ENDF/B-VIII.0 and present measured rate
of $^{159}$Tb(n, $\gamma$)$^{160}$Tb in the MESA simulation.
