Is it permissible to sell a house at a price higher than requested, while taking the excess without the knowledge of the principal?

If the principal specifies a price for selling the house, the fundamental principle is to adhere to it. However, it is permissible to sell it for more than the specified price, and the increase belongs to the principal, unless he grants it to you. If the principal says: "Sell the house for such-and-such, and whatever exceeds that is yours," then the increase is yours.