Well done, no complains from me. Only personal preferences, like board is too shiny or place lamp on an other spot. If a chess player needs to look at that reflection the whole day …
But you did a good job.
Great work! I love the details of the figures, especially the curvy Bishop’s hat, simplicity of the Knight’s shape (not overloaded, yet very recognizable, for my personal taste I’d play with ears, but not sure).
A question - did you use the smooth shading? And if not, can I ask why? Just curious.
On the possible improvements. Now this picture is just a show off of your modelling work (which is good on its own), but is it possible to change it into a more exciting image? One that tells a story? One of the ways to do it is to search internet for the chess pictures, find one that really catches your attention and or/inspires you and re-create it or build on it. Of course if you find its interesting.
As usual Thanks for the feedback! FedPete, on the shiny board I was trying to go for a glass top look but couldn’t figure it out. I will be fixing it though. VirtuMax, answer to your question is no because I never thought of using it to be honest. I am using a subdivision modifier on the pieces though. Also, I am sorry for not specifying that this is a WIP. I am still working on it I just wanted to get some feedback/advice like you guys have given me so that I can go back to working on it and apply it. Thanks guys I will update once I am done!
For the reflective surface you need something to reflect. In the real world you always have objects around, in Blender it’s just a light spot and absolute darkness 
As there is nothing to reflect (except the light), you poorly see a surface being reflective even you turn it on all the way in (and roughness out). One of the options is to use a HDRI image for the scene (it gives a surrounding to reflect).
Not using the smooth shading can be a personal choice. It’s not a matter of good or bad, but I can see the separate polygons on your figures, so I was curious if you left the smooth shading intentionally. Sometimes you go for realism, sometimes for that “digital” look.