part exchange 
British
noun [mass noun]
A method of buying something in which one gives an article that one owns as part of the payment for another, more expensive, article: he sold the car in part exchange for another vehicle...
- However, not all part exchange deals are equal.
- Dealers may dangle a ‘bargain’ in front of you, then try to make up the difference by offering you a poor deal on part exchange.
- I think the Pro might be pushing it too, but is not outside the realm of possibility, especially if I can do some kind of part exchange deal.
verb (part-exchange) [with object]
Give or take (an article) in part exchange: the caravans had been part-exchanged in favour of better-equipped vans...
- Fair enough, but he might want to consider part-exchanging it for a brain.
- John had part-exchanged my car for one for himself.
- This means your car is as quiet as the bicycle you part-exchanged to buy it.