The Zhukov was seen only in "Data's Day." In that appearance, the registry on the hull was given as NCC-62136 and its name was misspelled as "Zuhkov." These markings were not visible on screen and were later determined to be production flubs.
In the video game Star Trek: Bridge Commander, set in 2378, the Zhukov is assigned to Starbase 12 as a support ship. It escorts the USS Sovereign back to Starbase 12 after the latter suffered a breakdown of its warp systems. It can be later chosen to assist the player in a tactical attack at the Alioth system. It's commanded by the Andorian captain, Milus Verata.