High average power narrow-linewidth tunable solid-state lasers in the wavelength region between 2 to 3 μm are attractive light sources for many applications. This paper reports a narrow-linewidth widely-tunable laser system based on the polycrystalline Cr2+:ZnSe elements pumped by the repetitively-pulsed 2.1 µm Ho3+:YAG laser operating at the tens of kilohertz pulse rate. An advanced procedure of ZnSe-element doping and surface improvement was applied to increase the laser-induced damage threshold, which resulted in an increase of the output power of the Cr2+:ZnSe laser system. The high-average-power laser system comprised double master-oscillators and power amplifiers: Ho3+:YAG and Cr2+:ZnSe laser oscillators, and Ho3+:YAG and Cr2+:ZnSe power amplifiers. The output wavelength was widely tuned within 2.3-2.7 µm by an acousto-optical tunable filter inside the Cr2+:ZnSe master oscillator cavity. The narrow-linewidth operation at the pulse repetition rate of 20-40 kHz in a high-quality beam with the average output power up to 9.7 W was demonstrated.