Is it an adverb clause, a relative clause or a noun clause? "To get to New Zealand the fastest way"
The whole sentence is... To get to New Zealand the fastest way, you will have to fly from Copenhagen.
It's a PP, prepositional phrase, with preposition "for" understood. The object of the PP is a nominalized sentence with the complementizer "for-to" (compare "For you to get to New Zealand ..."). If the alternative complementizer "(Poss)-ing" is used for the PP object, the preposition "for" can be expressed: "For getting to New Zealand the fastest way, ..."