Answer:
My first keeps time, my second spends time, my whole tells time.
As round as an apple. As deep as a cup. All the king's horses can't pull it up.
Pirates put their booty in it.
If I have it, I don't share it. If I share it, I don't have it. What is it?
Alive without breath, As cold as death, Clad in mail never clinking, Never thirsty, ever drinking
My days are numbered.