Catalyzes the concluding reaction of the photorespiratory C2 cycle, an indispensable ancillary metabolic pathway to the photosynthetic C3 cycle that enables land plants to grow in an oxygen-containing atmosphere. Cytoplasmic D-glycerate 3-kinase that constitutes a photorespiratory bypass that alleviates fluctuating light-induced photoinhibition (PubMed:29129375). (R)-glycerate + ATP = (2R)-3-phosphoglycerate + ADP + H(+) Photosynthesis; photorespiration; 3-phospho-D-glycerate from glycine: step 4/4. Expressed in the light. Expressed in the dark. Isoform 1: Expressed in the light (PubMed:29129375). Isoform 3: Expressed in the dark (PubMed:29129375). Expressed in the light. Expressed in the dark. Belongs to the GLYK kinase family.