Need Advice

Hello, I have been having trouble with my boyfriend. He his still in contact with his ex. I dont think there is anything wrong with being in contact with ex but it makes me uncomfortable because In the beginning of our relationship he lied to me about still being with her. And he always lied to me about when he was with her. They are officially broken up now and she is seeing someone else. They still share a house together but he stays with me in my apartment all of the time. I know he no longer sees her as a girlfriend and me and him have been working really hard to grow our relationship. I know he is trying to change and work on thinks but it still makes me uncomfortable that they still talk and I still have trust issues with him. Im just not sure if I should work harder on it or just move on. I know I struggle with insecurity issues which can sometimes cause me to over think little things but I just dont know what to do. I would live is someone could give me some advice on what to do. Thank you