Supply of money remaining the same when there is an increase in demand for money, there will be:

With an increase in demand for money, people will deposit less money in banks. Hence, banks will increase the rate of interest to attract people to deposit money in the bank.

Alternatively, Supply remains the same, and an increase in demand for money will lead to more options to lend money for the banks. Thus, banks will lend money at a greater rate of interest to earn more money as there are more customers for the same amount of money.