The answer to this question will depend on what agreement you strike with the dealer and the nature of the contract you sign.

Usually, buried away in the terms and conditions of the sale, the dealer will reserve the right to change the price of the part-ex if they feel the value has changed due to market conditions or the condition of the vehicle has significantly changed.

The dealer will most likely give you a provisional part-exchange value now, which will be adjusted to reflect its condition and market value as/when your new car arrives. If you are unhappy with this arrangement then raise it with the dealer now and ask them to confirm the trade-in value in writing, with no scope for backtracking at a later date.