You need to use an article.  Use "a" if this is the first mention of a conservatory, and use "the" if the conservatory was previously mentioned, or is already known from context.  If everyone already knows what conservatory you're talking about, and if the name of the conservatory contains the word "Conservatory" [e.g., The Royal Conservatory of Music (Toronto, Canada)], then you should capitalize "Conservatory", just as we do with other proper names.