Updating old BitCoin-QT Core client V0.7 - 2017 Approach?
edit: [removed a part about upgrading. Lower part still remains relevant I think, so I think I will keep it there.]

I don't know of any place where you can download the latest compatible blockchain, but more importantly you should never want to do so! If you download it from some shady site, what guarantees would you have that the chain has not been tampered with, or that it will contain trojans, keyloggers or the like, which could lead to loss of funds/time. Just install the bitcoin client of your choice and let it download the blockchain through its connected nodes. It can verify the contents and make sure you are on the right chain.