I am an independent consultant and a Business Analyst who has been working in Banking and Finance and Technology industry helping them in Data Science, Organizational Development and Strategy development. I am now looking forward to focus on startups. How should I approach them and where will I find the right contacts to venture in startup industry?
Are you looking to charge or provide the services pro bono? As a Startup, we have lots of people that want to offer ideas and no money to pay them. So - in my opinion - the best way to position yourself is to offer pro bono services or to help put together networking sessions, meetups, and interest topics for entrepreneurs in the area (you could even charge a nominal fee to participate). There are other "consulting" type services that exist, and you should look at them as well because it may be good to latch on to some of their programming (like the Junto Institute in Chicago). Otherwise, join an accelerator and just start chatting with startups
Consider your consulting work as a startup and get a website. There are many tools for non-tech people to do this on their own, without using the help of a developer.
Promote this website as much as possible. Alejandro lists some here. I hope your work is not limited to your geo location but can be used by startups anywhere in the world.
Try to search at accelerators, like TechStars, 500 startups, Y Combinator etc.
You can try all the sites for freelance work - freelancer, guru, upwork, etc.
Freelancer is a very low price / low quality product (my feeling is there are no good advisors there) and is complicated to handle,
Guru has a very sporadi offers (no critical mass of clients),
Upwork is probably the best place you can find.
There should be other sites, but their job posting frequency is so low that you should not consider them attractive at all.
On all the site the competition is tough, and it takes time and patience to get good references and start generating recurring business. If you specialize in one or two key services, you can be very cost effective, and you build a base of promising clients (hopefully :))
Network your fingers to the bone. Start with a specialty industry/geograph.