Elizabeth Taylor's estate is applauding Taylor Swift for giving the late Hollywood legend a big-time shoutout in a new music video.

Taylor dropped the music vid for her hit single "Elizabeth Taylor" this week, and it's chock full of Elizabeth's most iconic scenes and dazzling diamonds.

A rep for Elizabeth's estate tells TMZ they're "thrilled" and "deeply moved" by Taylor's "extraordinary" tribute.

The estate's rep tells us ... "What makes this piece so remarkable is its pure devotion to Elizabeth’s legacy: composed entirely of archival film clips, from her iconic screen performances to candid moments, it is a celebration of Elizabeth from beginning to end, and an homage in the truest sense."

The statement continues ... "We are delighted by this celebration and the care with which Taylor Swift has spotlighted what so many have long understood: Elizabeth Taylor was a true icon, a trailblazer in every sense of the word. She lived unapologetically and on her own terms, embracing her public life with grace and courage while fiercely protecting the private world she cherished with family and friends. That balance, that duality, was one of her most remarkable qualities."

The new music video isn't available on YouTube ... just streaming services like Spotify and Apple Music.

ET's estate adds ... "If there is anyone navigating the extraordinary pressures of global fame with comparable authenticity and strength, it is Taylor Swift. The estate is honored that she chose to pay tribute in this way, and have no doubt that Elizabeth would have loved every frame of it."