Where is the harthome city gym leader

The Hearthome City Gym Leader can be found in the Contest Hall. She must be talked to in here before she'll appear in the Gym. She is also the 5th gym leader in the game if you haven't beaten four Gym Leaders yet then it's too early to battle her. If she is still not able to be battled try continuing the game till you've returned a key-item to Celestic Town.