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 (By similarity). L-cysteine + O-succinyl-L-homoserine = H(+) + L,L-cystathionine + succinate Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway; L-cystathionine from O-succinyl-L-homoserine: step 1/1. Belongs to the trans-sulfuration enzymes family. MET7 subfamily.