Is it permissible to exchange old gold for new gold while paying the price difference to the jeweler?

It is not permissible to exchange low-quality gold for high-quality gold with the payment of a difference, because that is usury (riba). The evidence for this is the story of Bilal (may Allah be pleased with him) when he brought good dates, and the Prophet (peace and blessings of Allah be upon him) said to him: "Oh, do not do that! That is exactly usury, exactly usury." The correct approach is to sell the low-quality gold for cash, and then buy the high-quality gold with that cash.