If you would like to book a discount for the customer after the start of the contract, you can go to the customer's contract details, clicking on "Perform Action" and then on "Up-/Downgrade".
In the "Up-/Downgrade" menu, select no(!) plan and no plan variant, but activate the checkbox "Inherit Start Date" in order not to change the contract and cancellation periods. Select the date from when the discount should be valid as "Date".
In the "Discounts" section of the menu, select the desired discount and add it, clicking the button on the right. Alternatively you can enter a coupon code that is linked to the discount. By clicking "OK" the discount will be added to the contract.