you can trade on a platform with a new york bitlicence, but as far as i can tell there aren't any.
Circle has had a BitLicense since 2015, but they pivoted away from Bitcoin. I think you can still send BTC and possibly other cryptos using it, but I don't think you can buy/sell anymore.
Ripple was awarded the second BitLicense in 2016. I used the Ripple interface to trade various currencies back in 2013, but they seemed to have made a lot of changes to the platform since then, so I'm not sure how you use it to trade now.
Most notably, Coinbase was awarded the third BitLicense. I heard that others, like CryptoFacilities, are in the process of seeking approval, but that's it for now.
That goes for all of the exchanges. Even the most well-funded exchanges in the world, like Coinbase, are incredibly unreliable -- APIs constantly dropping off, mismatching trade engines, constant server/website downtime and unplanned maintenance. By the standards of the stock or forex markets, the infrastructure around BTC trading is pathetic.
Sadly, this is one of the reasons why BTC-e was as popular as it was. It had one of the most reliable APIs and trade engines in the business.