Catalyzes the removal of elemental sulfur from cysteine to produce alanine. It supplies the inorganic sulfur for iron-sulfur (Fe-S) clusters. Plays a role in both tRNA-processing and mitochondrial metabolism. Involved in the 2-thio-modification of both 5-carboxymethylaminomethyl-2-thiouridine in mitochondrial tRNAs and 5-methoxycarbonylmethyl-2-thiouridine (mcm5s2U) in cytoplasmic tRNAs. [sulfur carrier]-H + L-cysteine = [sulfur carrier]-SH + L-alanine Expression is up-regulated at high-iron conditions. Belongs to the class-V pyridoxal-phosphate-dependent aminotransferase family. NifS/IscS subfamily.