As a detective, the first thing I would do is break down the crossword clue into its key components: “popular singer“, “recorded in Elvish“. The term “Elvish” immediately brings to mind the fictional languages created by J.R.R. Tolkien in his novels, such as “The Lord of the Rings”. I’d then think about which popular singer might be known for singing in a language like Elvish, and ENYA comes to mind. ENYA is an Irish singer known for her ethereal and otherworldly music, often featuring a mix of Gaelic and created languages. Her popularity in the 1990s and beyond would make her a likely candidate for a crossword puzzle aimed at a general audience. Putting all of these pieces together, I would confidently write in ‘ENYA‘ as the answer to this crossword clue.