obviously I understand the definition part "One who will succeed". But can someone tell me how the word play part works in this clue?
"with melody, we hear"
"Heir" is usually pronounced with a silent H, so sounds like "air". One meaning of the word air is a melody, such as "air on a g string". "We hear" is a common idiom in cryptic crossword clues for homophones ie "sounds like". So "melody, we hear" = "sounds like another word for melody" = "sounds like air" = "heir".