Don’t expect any changes overnight. Increasing your website’s Domain Authority is a game of patience and consistent efforts, which means one new backlink won’t magically bump your DA. However, there are two trends that you should know about.
Firstly, if your website has a low DA then it’s relatively easier to increase your authority with new backlinks. So a jump from DA 10 to 20 is easier than a jump from DA 80 to 90.
Secondly, a backlink from a high authority site has a quicker (and bigger) impact on your ranking than a backlink from a low authority site. High DA sites are crawled more often, allowing new backlinks to be discovered more quickly, and pass on higher link juice.