Very few examples are known of red supergiant runaways, all of them descending from the more massive O-type precursors, but none from the lower mass B-type precursors, although runaway statistics among B-type stars suggest that K-type runaways must be relatively numerous. We study HD 137071, a star that has been considered so far as a normal K-type red giant. Its parallax measured by Gaia and the derived luminosity suggest that it is actually a supergiant, whereas its derived distance to the galactic plane and its spatial velocity of 54.1 km s$^{-1}$ with respect to the local standard of rest suggest that it is also a runaway star. However, intrinsic limitations in determining the trigonometric parallaxes of cool supergiants, even in the Gaia era, require accurate spectral classifications for confirmation. We reliably classify HD 137071 as a K4II star establishing its membership to the extreme Population I, which is in agreement with the luminosity derived using the Gaia DR2 parallax measurement. Kinematical data from the Gaia DR2 catalog confirm its high spatial velocity and its runaway nature. Combining the spectral classification with astrometric information, a state-of-the-art galactic potential model, and evolutionary models for high-mass stars we trace the motion of HD 137071 back to the proximities of the galactic plane and speculate on which of the two proposed mechanisms for the production of runaway stars may be responsible for the high velocity of HD 137071. The available data favor the formation of HD 137071 in a massive binary system where the more massive companion underwent a supernova explosion about 32 Myr ago.
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