The nuclear level density is a fundamental quantity in nuclear physics, governing various nuclear reactions and astrophysical processes. In this study, we report on the collective enhancement of nuclear level density and its fade-out with excitation energy in the deformed ¹⁶¹Dy, obtained through an exclusive measurement of neutron evaporation spectra. The ¹⁶²Dy nucleus was populated via the transfer of a triton in a ⁷Li-induced reaction on ¹⁵⁹Tb. Statistical model analysis of the neutron spectra revealed a large collective enhancement factor of 42±2, consistent with microscopic calculations. This enhancement factor is similar to the one obtained for mass A ~ 170 in our previous measurement. The energy-dependent collective enhancement over a wide range of excitation energies was inferred by combining the present results with the available Oslo level density below the neutron binding energy.