Catalyzes the conversion of O-acetylserine to cysteine. Also acts as a sensor of cysteine availability in the signal transduction pathway modulating CymR activity. When cysteine is present, the pool of O-acetylserine (OAS) is low, which leads to the formation of a CymR-CysK complex and transcriptional repression of the CymR regulon occurs. In the absence of cysteine, the OAS pool is high and the CymR-CysK complex is mostly dissociated, leading to a faster dissociation of CymR from its DNA targets and the lifting of CymR-dependent repression