This is becoming more common in regulatory law in Canada, but it’s unnecessary.
It’s fairly old – OED gives citations going back to the mid nineteenth century. The word is listed there as an Americanism.
The Law Society of Ontario has begun to use it: ‘Licensure is the official recognition by the Law Society that a candidate has met all the qualifications specified by the Law Society and is, therefore, approved to practice as a lawyer in Ontario.’
The more usual licensing (which the LSO also uses) would do perfectly well. (And I’d prefer to see practise for the verb, practice for the noun.)
I wonder if licensure was coined to make the process of getting a licence to do something sound fancier and somehow more legalistic.
As lawyers, we should try to get away from words and phrases that our non-lawyer readers (and listeners) wouldn’t normally use, much less understand – especially when there is a non-lawyer way of saying things that they’ll actually get.