High-average-power narrow-linewidth tunable solid-state lasers in the wavelength region between 2 and 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 repetitively pulsed 2.1 µm Ho3+:YAG laser operating at a pulse rate of tens of kilohertz. An advanced procedure of ZnSe element doping and surface improvement was applied to increase the laser-induced damage threshold, which resulted in an increase in 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 means of an acousto-optical tunable filter inside a Cr2+:ZnSe master oscillator cavity. The narrow-linewidth operation at the pulse repetition rate of 20–40 kHz in a high-quality beam with an average output power of up to 9.7 W was demonstrated.