It is natural in any relationship to explore your partner's interests, even if you're not particularly fond of them. Rock and roll may not be the dominant genre in your playlist, but if your outgoing lover has been looking forward to a Coldplay concert, why not tag along with them? Even if it means not sticking around for the entire show, attending indicates that effort is being made. There is a good chance that your extrovert will do the same for you on those nights when you only care to watch the latest Hulu docuseries.
An extrovert soul is fed by interactions with others. Therefore, don't be surprised if Wednesdays after work are designated for happy hour with coworkers while Sundays are reserved for brunch with friends. This is what replenishes them, keeping them in a positive space. Not saying an introvert should be present for each outing, especially if they are already feeling burned out. However, joining the fun once a month can draw you closer to your partner by allowing you to meet those closest to them. This offers more insight into the type of energy they enjoy being around. But be sure that your hobbies are being explored as well and on an equal level.