The correct option is C Chris Hipkins, who recently became the Minister of Education, hails from a place called Hutt Valley in the Wellington Region.
A noun clause is a dependent clause that functions as a noun. It usually
begins with what, whatever, whom, that and other such relative
pronouns. A noun clause can act as a subject, object, predicate
nominative or object of a preposition, in a sentence.
When a noun or its equivalent is in apposition to another noun/its
equivalent, its sole purpose is to provide extra information about that
noun/equivalent.
The question requires a noun clause to be made out of: Minister of Education. This can be seen in option B: "who recently became the Minister of Education" is a noun clause; it begins with a relative pronoun "who" that also functions as the subject, the verb "became". Hence option B is correct.
Option A is incorrect because "the recent minister of Education" is not a noun clause, it is a noun phrase.
Option C is incorrect because "became the Minister of Education" is not a noun clause, it functions as a predicate (a predicate can't be a noun clause because it contains the main verb, the noun clause does not include the main verb).
Option D is incorrect because "becoming the Minister of Education" is not a noun clause, it is a noun phrase.