Catalyzes the formation of L-cystathionine from O-acetyl-L-homoserine and L-cysteine. Cannot use O-succinyl-L-homoserine as substrate. Also exhibits O-acetylhomoserine thiolyase activity, catalyzing the synthesis of L-homocysteine from O-acetyl-L-homoserine and sulfide. L-cysteine + O-acetyl-L-homoserine = acetate + H(+) + L,L-cystathionine hydrogen sulfide + O-acetyl-L-homoserine = acetate + L-homocysteine Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway. Homotetramer. Up-regulated at the transcriptional level when sulfate, cysteine, cystathionine or homocysteine are the sulfur sources. Repressed by methionine. Cells lacking this gene are unable to grow in the presence of sulfate or cysteine as sole sulfur source, whereas their growth in the presence of homocysteine, cystathionine or methionine is similar to that of the wild-type strain. Belongs to the trans-sulfuration enzymes family.