Conneely, who plays his club rugby for the Galway city team Corinthians, came through the Connacht academy and was part of the Connacht Under-20 side that took the Grand Slam in the Interprovincial Championship during the 2011–12 season. He joined the senior side ahead of the 2013–14 season, signing a development contract. He had already featured for the province's second-tier side, the Connacht Eagles, in the semi-professional British and Irish Cup.