At certain levels, Barbarians gain additional Rages to use between Long Rests. My question is, when can these additional Rages be used? The PHB seems a little unclear on this.
Once you have raged the number of times shown for your barbarian level in the Rages column of the Barbarian table, you must finish a long rest before you can rage again.
This description doesn't really seem to account for levelling up between long rests. With that, there seem to be two options:
The Barbarian can use their additional Rage immediately after levelling up. In this option, the additional Rage comes in as an unused Rage. This option uses the idea that if a level 11 Barbarian has raged 4 times, he is out of rages. If after he finishes his 4th Rage, he levels up and becomes a level 12 Barbarian, he would then gain a 5th Rage that is unused. Being as he has only raged 4 times since his last Long Rest, it would stand that he would have 1 more Rage.
The Barbarian must wait until after his next Long Rest to use his additional Rage. In this option, when a Barbarian gains a level and an additional Rage, it is accounted as apart of the Barbarian's total Rages, not available Rages. This option is similar to a players Hit Points when they level, as in the player gains Hit Points to their Hit-Point Maximum, but not their Hit Point Total.
Each time you gain a level, you gain 1 additional Hit Die. Roll that Hit Die, add your Constitution modifier to the roll, and add the total to your hit point maximum.
Levelling mechanics at my table:
The Rogue gets their additional sneak dice right away. The same goes for the Monk and their additional Ki points. Casters, while they get their additional spell slots immediately on level up, they must wait until a rest (short or long depending on the class) and then prepare spells for any new level of spells they have gained (ie: they have 1 level 5 spell slot, but no prepared level 5 spells).