提高 and degree complement
提高 literally means "lift/raise sth. up". Its extended meaning is improve or make a progress.


  他提高得很快


In this sentence, you have used the extended meaning(improve) of 提高. The whole sentence can be translated to: He improved rapidly/very fast. 

In my opinion, if you use its extended meaning, then it's not a 离合词 because you can't separate it. Well, it can be considered as a 离合词 when it denotes its literal meaning(lift up), because it is separable . For example, you can say 提得高.  

PS. As the comment pointed out, 提得很高 is more common than 提得高 in practice.