So the machinery of pursuit was the organized way that Harriet Tubman selected slaves to travel on the Underground Railroad
Assuming the italicized clause is <em>Since its establishment, </em>the correct answer here is elliptical clause.
Elliptical means that a word which would normally be part of a sentence is excluded, usually for stylistic reasons. Here, the verb is missing, which is why it is elliptical. The question is oddly formulated too - given that there is no verb here, it cannot be a clause, but rather a phrase, but since there is no such option here, then the correct answer is elliptical clause.