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The advent of sensitive low-frequency radio observations has revealed a number of diffuse radio objects with peculiar properties that are challenging our understanding of the physics of the intracluster medium. Here, we report the discovery of a steep-spectrum radio halo surrounding the central brightest cluster galaxy (BCG) in the galaxy cluster SPT-CL J2031−4037. This cluster is morphologically disturbed yet has a weak cool core, an example of a cool-core/non-cool-core transition system, which harbours a radio halo ∼0.7 Mpc in size. The halo emission detected at 1.7 GHz is less extended compared to that in the 325 MHz observation, and the spectral index of the part of the halo visible at the 325 MHz to 1.7 GHz frequencies was found to be −1.35 ± 0.07. Also, P_1.4 GHz was found to be 0.77 × 10²⁴ W Hz⁻¹, which falls in the region where radio mini-haloes, halo upper limits and ultra-steep-spectrum (USS …