New hearts, so far, come from new interactions available in the updates. So you should not have to restart the game to get them. But you might have to go back and do some things with the character you haven't done yet to meet all the requirements.
For example, to get Logan's 2nd heart you have to have asked him about his work and helped him with it at least once (among all the other requirements). That interaction has been around since at least .30 when I started, but only you know if you have done it or not. It should not be too late to do it if you haven't.