If your trade-in was independent of purchasing a new device, you can begin the process again.
If your trade-in was initiated when purchasing a new device (anticipating that the trade-in value would be deducted from the purchase price) - if the order itself has been completed and you have received the goods, it is now too late to return the trade-in. In such circumstances you will be charged the full amount of your order.
You can however, start a stand-alone trade-in - the value of which will be returned to you by way of an Apple Gift Card that can be redeemed against a future purchase from Apple, including Apple subscription services.
Otherwise, the only way to "reset" the process is to return your new purchase (if applicable) to Apple for refund - which must be completed within 14-days of your new purchase shipping to you. After receiving your refund, you can start again.