I was able to check out the TV at https://www.sony-asia.com/electronics/support/res/manuals/4562/45623121M.pdf and only see 1.x ports.
So the answer is maybe. You need to be very specific about the 4K UHD BR Disc player and since that's not listed I can't answer.
I will write these players do play DVDs. But I can't check if the model you are looking at demands HDMI 2.x connections. Not all do but let's check it out.
I have a FHD tv (Sony KLV-40R562C). Can I purchase a 4K UHD Blu-ray Disk player. Will it be able to play old (or in vouge) DVDs and will my current TV be able to show me the DVD's content? Since this TV is not a 4K TV, I will not be able to see 4K content.