" You could add "fruit" but it is unnecessary because just "papaya" often means the fruit. For example, if I say "I am going to buy a papaya", it is clear for people to understand that I mean that I am getting the fruit. " Here, it is better to include either "tree" or "plant" because you are referring to the tree or the plant of papaya (which bears many fruits).
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.