I have a website which is around 7 years old. I haven't posted much content earlier. Is it Ok to start posting contents on this website and do SEO or Is it better to start a new website and do SEO on it
Well it certainly depends on the domain. What is its name & how much is it important in your niche (according to relevancy)? How much content does it already have and what links does it have? If the content is worthwhile and the links to it is live & relevant. Then I don't see what is the reason about starting a whole new site.
Domain age is only relevant if the site has a history with backlinks. If the domain was registered but nothing was ever done with it then you're basically starting with a new domain name.
I think there is no need to start a new website when you already have the live website from the 7years. All you need to do is fix the OnpAge error of the websites first and change its design too as it is 7 years old website and make some changes that are required, then update the content and replace the outdated content with the new one. And, make an index request again in with the webmaster's tool.
I am agree with Sumit_Singh you do not need to build a new website but you have to redesign and update whole content from your old website and start SEO for that(old) website. It will perform well than new website.