The phrase "add the legacy of" is correct and usable in written English.
It can be used when discussing the incorporation or inclusion of historical or significant elements into a current context or project.
Example: "In our new initiative, we aim to add the legacy of past innovators to inspire future generations."
Alternatives: "incorporate the heritage of" or "include the tradition of".
You can hear Brooklynese spoken in parts of New Orleans and Cincinnati, Labov added, the legacy of the New York bankers who moved to those cities in the nineteenth century to finance the cotton trade.
But none of these works seems likely to add to the legacy of his grand-scale, big-screen dramatic frescoes — the films that are being celebrated in the BAM retrospective.
Taken together, the five sports are an innovative combination of established and emerging, youth-focused events that are popular in Japan and will add to the legacy of the Tokyo Games".
Jonny Sweet: Mostly About Arthur Pleasance Courtyard Having bagged the role of David Cameron in a More 4 production, Sweet's stock is up, but hopefully he will still have time in the future to add to the legacy of this quirky debut show about his deceased – but fictional – brother, Arthur, whose job it was to write the blurbs on the back of novels.
BBC Music: How do you want your book to add to the legacy of Kurt Cobain and Nirvana?
To Elizabeth's evocation of the trumpet and snare drum of the colonial military bands (which ultimately became the basis of the jazz instrumentation in New Orleans), I would add the vocal legacy of the military drill, which evolved into the gruff vocal style of dancehall reggae.
The victory also added to the legacy of Hiller, the former Maryland star, who will be inducted in the U.S. Lacrosse Hall of Fame as a player.
But now an unsettling asterisk must be added to the legacy of Ernest C. Withers, one of the most celebrated photographers of the civil rights era: He was a paid F.B.I. informer.
"Independent film is, when you think about it, pretty American," he said, adding that the legacy of independent filmmaking - movies made outside Hollywood's major film studios - was to give a voice to notions of freedom, liberty and dissent.
