Catalyzes the formation of L-cystathionine from O-succinyl-L-homoserine (OSHS) and L-cysteine, via a gamma-replacement reaction. In the absence of thiol, catalyzes gamma-elimination to form 2-oxobutanoate, succinate and ammonia. L-cysteine + O-succinyl-L-homoserine = H(+) + L,L-cystathionine + succinate Binds 1 pyridoxal phosphate per subunit. kcat are 700 min(-1) and 460 min (-1) for the gamma-replacement and gamma-elimination reaction, respectively. Optimum pH is 7.8 for the gamma-replacement reaction. Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway; L-cystathionine from O-succinyl-L-homoserine: step 1/1. Homotetramer. Belongs to the trans-sulfuration enzymes family.