Translation:You are not washing dishes where the new waiter is standing.
The English version does not require the "there". It is unnecessary. It is already covered by "where" which could be thought of as "at the/that place where". "At the/that place" being "there".
But the Hungarian version wants to emphasize the "that place" part. It specifically wants to negate that part. "NOT at that place", that is, not there: "Nem ott".
And, in general, this "ott" part of the construction is usually necessary in Hungarian. Sometimes it can be omitted but usually it is not. In English it can usually be omitted. It may even sound weird if it is not.