I do not know any expression. but this person can be called a mischief-maker ;
Macmillan Dictionary : someone who enjoys causing trouble or disagreement
I , of course , would prefer to use stirrer. it is a more exact but informal. it depends on your context.
Macmillan Dictionary : someone who tries to cause trouble between other people
EDIT: I have found a appropriate expression: play sb/sth off against sb/sth
Collins Dictionary : If you play people off against each other, you make them compete or argue, so that you gain some advantage.
Example:Gregory would interview them, and would play one off against the other