The promissory note is a quest item used in The Fremennik Trials. It is obtained by giving 5,000 coins to Askeladden in Rellekka. The note can then be given to Thora the Barkeep in exchange for a legendary cocktail.
The promissory note is basically a contract to stop Askeladden from entering the bar because he is underage. However, as he is Fremennik, he will be able to enter the bar after completing his trials, as he will get a new Fremennik name.