How are hit dice added when leveling takes place?
Hit Points are pretty straightforward in that the new hit points that are gained through a level advancement are only added to the character's "maximum hit points" at that time (PHB, p. 15). Their "current hit points" will not also go up until they take a long rest or use some other means to raise their "current" hit points (short rests, healer, potions, etc., etc.).
However, the PHB is a little more vague on hit dice. When a hit die is gained through a level advancement, how this should be added? Is it like hit points and only be added to their "maximum hit dice" until a long rest allows the character to regenerate some of their current hit dice? Or is the newly gained hit die added both to their "maximum hit dice" and the "current hit dice" they have available to use?