Hey mikahlia_1! This is a great question. If your old iPhone is paid in full, there's no need to turn it in to JUMP! to the new iPhone, since the purpose of JUMP!ing instead of a standard upgrade is that you turn in your existing phone and the remainder of your EIP balance is forgiven when you start the EIP for the new phone - so you're only paying for one phone at a time.
If you still owe on your old iPhone, then you may keep it and still upgrade, but you'll make payments for both phones at once until the old one's paid off. You might also have a higher down payment required up front on the new phone, because the intention is to enable customers to finance one phone and accessories per line - so there's a per-line credit limit, and if you still owe on your old iPhone, that balance would eat up some of your available credit.
Hopefully, your situation is more like the first one I described; in which case, gift away! Thanks for reaching out here, please let me know if you have any more questions.