[1] Alexander started to play drums at the early age of seven years old surrounded by jazz musicians like Freddie Hubbard, Reggie Workman, Gary Bartz and Kiani Zawadi.
At the age of nine he was studying drums under the leadership of master drummers Rudy Collins, Andre Strobert and Walter Perkins at the New Muse music school in Brooklyn, New York.
At the same time, he started to study drums with Justin DiCioccio at the La Guardia Music & Art High School in New York.
Alexander performed domestically and internationally with: Abbey Lincoln,[4] Betty Carter, Roland Alexander, Roy Hargrove, Rodney Kendrick,[5][6] Branford Marsalis, Danny Mixon, Gary Bartz, Carlos Garnett,[7][8] Reggie Workman, Bill Saxton, Kenny Davis, Lonnie Plaxico, Bill Lee, Tommy Turntine, Bill Saxton, Gary Bartz, Eddie Comes, Murgrew Miller, Taurus Mateen, Roland Alexander, Eric Alexander, Reggie Workman, Branford Marsilis, Wynton Marsilis, Gerry Eastman,[9] Ron Burton, Paul Brown, Juni Booth, Kiani Zawadi, Eddie Henderson, Abbie Lincoln,[10] Betty Carter, Sweet Georgia Brown, Fred Ho, Sam Furnace, Hank Jones, Roy Hargrove,[11] Benny Green, Christian McBride, Steven Scott, JD Allen, Peter Bernstein, Monte Croft, Don Sickler, Bobby Watson, Clifton Anderson,[12] Tadataka Unno, Amin Salim, Ronnie Mathews, Dywane Burno, Justin Robinson, Curtis Lundy, Michael Marcus,[13][14] Sonny Simmons[15][16] and many more...[17] He has a musical group called The Taru Alexander Quartet.
Sideman [33][34] In 1996 Taru was honored with a proclamation for his musical achievements by Brooklyn borough president Marty Markowitz alongside jazz drummer Max Roach.