From the beginning of this relationship, you'll both sense that it has the potential to deepen into something serious. You had a serious, long-lasting connection in another life, and the lessons you learned then paired with the stability and trust you established together have led to the sense of seriousness and dependability you'll both feel in this life. You'll feel somehow responsible for your partner, as if it's your job to take care of them in some way -- making sure that their commitment needs are met, for example.
You'll take this relationship seriously, and they'll sense and appreciate that fact, most of the time. Sometimes, of course, they might feel frustrated with how heavy your interactions are. Why can't you two just lighten up a little, and have a fun, flirtatious encounter? Even if they feel these frustrations, though, they'll still feel a sense of obligation that will keep them by your side. Now, you might be thinking that obligation isn't the warmest, most romantic bond a couple could have, and you're right: That sense of duty and commitment comes from your past-life connection, and creates a strong, if unromantic, bond. But in this life, you can learn together to create a bond that's just as committed but that leans more toward light, fun, warm, affectionate encounters. One step toward that goal will be not to commit until you're certain that you're doing it for the right reasons: not out of obligation, but out of a genuine desire to be together and love one another.