[2] After completing his education, Elvers worked as music dealer for the Merseburger Verlag [de] in Berlin.
In 1965 he left the post to become director of the Felix Mendelssohn archives at the Berlin State Library's Staatsbibliothek Preussischer Kulturbesitz.
He was promoted to director of the music department at the Berlin State Library in 1967; a position he held until his retirement in 1988.
[2] During his years in the music department of the Berlin State Library,Elvers was - partly together with Hans-Günter Klein - responsible for a number of catalogues that are now considered standard reference works, including Ludwig van Beethoven (1970), Felix Mendelssohn (1972), Fanny Mendelssohn (1972 and 1983), and Johann Sebastian Bach (1985).
He built up one of the most important collections of autograph letters, manuscripts and artifacts of Felix Mendelssohn Bartholdy and his family, which he donated to the Stadtgeschichtliches Museum Leipzig [de] in 2009.