Prospecting licence 3313 is in county Kilkenny to the north east of Vedanta's Lisheen mine and Lundin's now closed Galmoy mine and to the south of the Rapla mineralised zone explored by Arcon and Lundin, the company said.
Connemara chairman John Teeling said: "This part of Ireland, which contains the giant Lisheen zinc mine and closed Galmoy mine, has always been rich in zinc.
"Our previous drilling has been focused on the north west of the block and we have potential targets to the south east.
"We are excited that the zinc industry is finally coming back to life with a supply deficit, which is likely to continue for some years.
"This licence adds to the high quality portfolio of licences across Ireland held by Connemara."