"I made it my prime objective settling the matter." - unacceptable extraposition

Solution 1:

It is my prime objective to settle the matter.

My prime objective is to settle the matter.

The first example introduces "it" which serves to move the subject away from the subject position.

The second example eliminates the need for it, which makes the sentence more concise. For general usage, I don't think it matters. For academic or certain other genres, where the rule is to be more precise, it is helpful to eliminate the "it." Ultimately what you place in subject position is a matter of emphasis, for instance:

Settling the matter is my prime objective. Moves the emphasis from 'my prime directive' to:'settling the matter.' Though the distinction in some cases is negligible.

A good source for the 'extraposition' is: https://www.thoughtco.com/extraposition-grammar-term-1690626

My favorite grammar book is The Grammar Book 3rd Edition Dianne Larsen-Freeman and Marianne Celce-Murcia. (p.25) Theme/Rheme (Deals with emphasis)

I teach composition for academic English as a graduate student in a University, though I make plenty of mistakes, regardless. It is a general principle of academic English to be as concise as possible; However, the rules are constantly changing. My understanding is that the genre informs the type of usage for a sentence so that what is appropriate in one genre may not be in another.