Carew as a surname has famous namesakes that include Nobel prize winner John Carew Eccles, Baseball Hall of Fame member Rod Carew, and poet/author and diplomat Thomas Carew. In literature there is the character Mad Carew in The Green Eye of the Yellow God by Milton Hayes.
I find this an interesting surname alternative for Andrew, which is eternally popular (#34 last year). It could honor an Andrew in the family tree with its spelling, or a Carey. It has no U.S. data, making it extremely rare.