A predicate noun is a noun that provides more information about the subject of the sentence, here 'headmistress' is a predicate noun for the subject "Mrs Trent". The article is omitted before predicate nouns that denote a unique position, there can be only one headmistress in a school. Hence the article is omitted from the sentence and option D is incorrect. Option C is the correct option as there's no article before 'headmistress'. Options A and B are incorrect because the article (a, the) is to be omitted from the statement.