See How do I blend 2 lightmaps for day/night cycle in Unity? for a previous question about fading 2 lightmaps for day/night cycles. It includes an answer that seems to indicate how to do it. Your challenge will be to get the current time, figure out how much day/night sky you want given that time, and make it so.
In the answer given to the linked question, the shader has a "_Blend" value that you can set between 0.0 and 1.0. 0.0 is fully one skybox, and 1.0 is fully the other. What you'll want to do is have it be one value during the day, and the other during the night. Then as the sun goes down, change to the other. As it rises the next day, change back.