The question of what actually triggers a 7-result SERP is definitely complicated, especially as Google expands into Knowledge Graph and advanced forms of entity association. There's definitely no simple on-page SEO trick to get the 7-result SERP
In August of 2012, Google launched 7-result SERPs, transforming page-one results. Here are a few examples of the various forms the 7-result SERP takes these days.
1) Search for “some ecards”
2) Here’s a 7-result SERP with one image pack and six organic listings – the search is “pictures of cats”
As such there is no evidence that it effects rankings but it do effect on the ranking reports. My best advice is to spot-check the SERPs for your main keywords. Don't just rely on rank-tracking tools - they may tell you that you're in the #8-#10 spot, but they won't tell you whether your SERP cut off after #7. If you're sitting on a lot of #8 keywords, you may find yourself suddenly on Page 2.