"... having never learnt" is a present perfect particple. - simplified version Many priests have never learnt how to form intimate relationships with women. These priests are ill-prepared for marriage. - simplified version with a relative clause The priests who have never learnt how to form intimate relationships with women are ill-prepared for marriage. - simplified version with a present perfect participle Many priests, having never learnt how to form intimate relationships with women, are ill-prepared for marriage.

I think that it is an a appositive. And appositive is a phrase that adds additional information, usually between two commas. Example:”Many Americans, having never traveled outside the United States, have little understanding of other countries.” Appositive phrases normally come in the middle of a sentence. The appositive phrase in your sentence is unusual in that it comes at the end of the sentence.