Instead of focusing on link building, I would suggest focusing on building quality content that is better than the top 3 placement in search for your keyword. Optimize your website for search internally (remember to add your website, sitemap to search console)
A good expired domain is pretty old school, it doesn’t work the way it used to be. And make sure these domain doesn’t have a doggy link that could potentially affect your website even further.
one thing to note that SEO is a long term game, to compete with an existing competitor requires creativity in seeking for the link. One of the best ways is to use tools like ahref and put your competitor’s domain in and see what keywords they are ranking for and also where they get their links from. This way you can also figure a way to get links from these sites.