Spell Levels are currently limited to Level 9. There is no class that has a 10th level spell slot and there are no rules that suggest there is a 10th level spell slot. Neither are there current 10th level spells that could use a 10th level spell slot.
The PHB (page 201) clearly states:
Every spell has a level from 0 to 9.
and (emphasis mine from @MichaelPolitowski)
When a character casts a spell, he or she expends a slot of that spell’s level or higher, effectively “filling” a slot with the spell. You can think of a spell slot as a groove of a certain size—small for a 1st-level slot, larger for a spell of higher level. A 1st-level spell fits into a slot of any size, but a 9th-level spell fits only in a 9th-level slot.
This clearly states that there is no 10th level (currently) spell that you can cast. While it doesn’t explicitly state there is no 10th level slot, the implication is that without 10th level spells there aren’t 10th level slots – otherwise there would be upscaling options allowing you to utilize that.
One can reasonably extrapolate how it’d work, but the current rules do not include 10th level and there are no other examples list going to a 10th level (such as examples that list surpassing 20 for an Ability Score.)
The following phrase from the Book description does not create a new spell slot level, it simply upcasts to one level higher. The current cap of a 9th level spell remains:
any spell slot you expend to cast a cleric or paladin spell counts as a spell slot of one level higher.
Unlike the rules around Ability score raising with the Tomes/Manuals, this book does not state that it increases spell levels beyond the current cap of 9th.
A free upcast
What this book does do is give you a free upcast without having to use a higher level slot. That’s still a pretty great benefit without having to create a 10th level spell slot that just doesn’t exist in the current rules.
The stated benefits are all still applicable and do not require generating an unlisted option (10th level spell slot) in order to be useful and/or work.
Interactions to consider and the Slippery Slope
If you do allow this in your games, be aware that this changes Counterspells and Dispel Magics. A simple fix, but just something to be aware of.
And for a warning, if this allows 10th level, then why couldn’t someone create a 10th level scroll? Or an 11th? Once you’ve confirmed the existence of 10th level, then that level now exists and must be accounted for.