The question should be clear enough from the title.
Also: What are we supposed to call one who ousts? [If this warrants another question, I will edit this out and open another question.]
An ouster (noun) is an ejection from an office or a position. Etymonline gives its derivation thus:
early 15c., from Anglo-Fr. oster (late 13c.), O.Fr. oster “put out, keep off, remove, avert” (Fr. ôter), from L. obstare “stand opposite to, block, hinder,” from ob “against” + stare “to stand,” from PIE base sta – “to stand” (see stet).
So the noun derives from the Anglo-French meaning, first and foremost in the sense of a “putting out” of someone, and it has come down to us as a handy synonym of “expulsion” or “impeachment” with the more general sense of relieving officials of their positions.
That said, ouster could be used in both senses: As someone who ousts someone else from a position, and the act of ousting that person. But the use in the former sense would be uncommon and not readily understood with no supporting context.