From what I'm understanding from your question you're asking how long it would take from the time that you gain a natural backlink to your site to the time that you should recieve a rank increase, and in turn, more traffic?
Unfortunately SEO doesn't work like that and it can't really be quantified in terms of single links. There are more than 200 ranking factors for Google now and links, albeit still an important ranking factor, is one of many that you need to look at in order to increase your visibility on the web.
There's no hard and fast rule to be able to drop a link and then see extra traffic. In some cases this may never happen, in other cases it works a treat. it really all depends on the link power and what the anchor text is along with other factors.
Search engines are complicated beasts, it's best to go for quality content and continue producing this content, share it to social media with the hope that it will get shared more via other websites which in turn will give you a more natural looking backlink profile.
Consistency is key here. Don't just get one link and then wait, build content then build more content, then more, then more.
Hopefully you get the idea.