Primary school teacher Elsie Clarke discovers that she has magic and is visited by a Middleman from the AMP (Association of Magical Practitioners). [Has magic? Like as in a disease? Do you mean, ...Elsie Clarke discovers she has the gift of magic and is visited..., or something like that. For whatever reason, that 'has' seems odd]
Everything seems wonderful until they discover [word echo]
that one of her fledgling gifts is prophecy, because something is killing prophets. [That sentence didn't make sense. Someone is killing prophets and that's how they discover her gift?]
Elsie needs to use her new power, and pierce the veil that hangs over the future to uncover who wants her dead and why. [Good.}
Colwin Throssle, a wizard with the unusual ability to control water, has been a Middleman for six months. Standing between the magical community and everything else[comma]
the Middlemen are underpaid, undermanned, and unappreciated - more social workers than police. Then there are the last five years which Colwin really does not want to think about, got married, moved abroad, painful breakup, but the details are weirdly vague. [That sentence is a bit odd. The vague part is confusing - to me. Maybe you should start out his introduction with that bit of information?]
Now he needs to keep Elsie alive, and teach her what magic he can, until he can palm her off as someone else's apprentice. [I think it would sound better if you wrote that last sentence: ...while he tries to palm her off to some other Middleman. Or something like that...I'm not being very helpful, am I?]
Together Elsie and Colwin fend of the attacks of an organization known only as The Unseen, a group of magic users who have achieved immortality and periodically destroy any magical institution that might rival their power. The Unseen plan to destroy the AMP at its upcoming 50th anniversary celebrations, which will see the bulk of the magical community gathered. Only a living prophet can hope to foresee the terrible nature of their attack.
Even as this happens[I would put a comma here]
goblin asylum seekers are pouring through into England [this is the first mention that we are in own world, or a fantastical version of our world, I think this bit of information should come sooner]
as terrible powers stir in faerie. And one of those terrible powers is Colwin's ex, who would not be thrilled to see him practising his awkward charms upon his new apprentice. [What? He's flirting with Elsie? This should be hinted at in the paragraph above, me thinks]
Because his faerie Princess is in the running to become a faerie Queen, and faeries don't believe in divorce. [What? His faerie Princess? You mean his ex-wife?]
Wet Knight is a 100,000 word(ish) urban fantasy novel that will appeal to fans of Jim Butcher's Dresden Files or Kevin Ahearne's Iron Druid Chronicles.
[I would re-arrange this last sentence a bit. Maybe: At 100,000 words, Wet Knight is an urban fantasy novel...]