The correct option is A Emeritus
An Emeritus is one (of the former holder of an office, especially a university professor) having retired but allowed to retain their title as an honour. For example, "emeritus professor of literature". Hence, Option A is correct. Among the rest of the options, honorary means conferred as an honour, without the usual requirements or functions, sinecure means a position requiring little or no work but giving the holder status or financial benefit, retired means having left one's job and ceased to work. These do not express the intended meaning, hence incorrect.