The most important aspect of getting organic traffic these days is matching the intent of the search term atleast as good as your competitors. If you can't do this, don't waste your time, move on to another keyword where you can match it properly.
Check out this related post to learn more about how to find KGR keywords.
Do on page optimization similar to competitors, but make sure you are not over optimized. For example, if competitors have the exact keyword phrase in the title and once in the body of the page, start off exactly the same. With longer search terms, 3-4 words or longer, you may not want the exact query on the page. I always use my competitors as a road map, but with longtail keywords, I always break up the title so it includes the individual words, but not in the exact order. You can use a tool like Page Optimizer Pro or Surfer SEO to quickly determine if your content is on par or needs some adjusting.
Perform a (site:domain.com "keyword") query on Google to determine the most relevant pages on your website. These will be the best pages to add internal links to your new page. Don't go over board on the anchor text, it shouldn't be needed since the pages are already relevant to your keyword. Use an anchor that is descriptive and non spammy.
Now your KGR page should be optimized, but not overoptimized. It will have a couple very relevant internal links. That should get you close. Give it a couple weeks and see if Google is testing your page up the rankings at all. If they are, leave it be until it settles out. If needed use one of the on-page SEO tools mentioned above to increase your on page relevance. You could also add another internal link or two as well.
Repeat this process with more KGR keywords and you will be well on your way to building a nice baseline of organic traffic that is diversified across many pages. Thats always a bonus if you decide to sell the site since have a lot of traffic to just a few pages is much riskier for a potential buyer. Over time you can slowly increase the search volume ranges you are targeting.
