Google Discover Vs Google Search
Google Discover shows on mobile devices on new tabs in Chrome. It shows topics that people have been browsing recently.
In Google Search keyword phrases are the main ranking factor, whereas Discover is about topics people have recently looked at.
One study found 46% of the pages in Discover are on news websites and 44% eCommerce. I have personally found the pages I see are usually recently made ones. Therefore, we probably won't see existing content on Discover. New blog posts should be written with Discover in mind.
Tracking Performance on Google Discover
In Google Search Console on the left of the page you will see "Discover". In here you can see recent statistics.
How to get more traffic from Google Discover
Discover is based on topics. Therefore, it would be prudent to use a thesaurus to include variations on keywords to cover different words used for different topics. This can also be done by typing a keyword into Google and looking at the text in titles for the different pages. Also at the bottom of the search results you can look at "Related searches".
Add the max image preview code for better visibility in Discover:
Pages with this code show a larger image in Google Discover. This results in 3 times the number of clicks, which will be a factor on whether Google shows the page in Discover. To get it showing you could show your web developer this video: https://www.youtube.com/watch?v=2qbXAk7FAAo . Featured images on new content should be at least 1200 pixels wide.
Google Ads for Google Discover:
You can try running Google Ads for Discover. This is done in the Google Discovery ad campaigns, which also target YouTube and Gmail.
Should you rely on Google Discover?
Looking at client's performances, only the ones actively blogging are getting traffic from Discover and it is in very small amounts. It is worth keeping in mind when creating new posts, but Google Search will always bring in almost all traffic for a non-news and non-eCommerce website.
It is worth writing some posts for anything which could count as news e.g. factual, non-promotional content. Keep in mind relevant keywords so that the post counts as one catering to topics people are searching for.