show that you are sorry for something
expiate - compensate
To ‘expiate’ means to atone for something you have done wrong by accepting fault or punishment willingly, or by doing something to make amends. This formal word implies a feeling of guilt and the urgent need to absolve oneself through words or action. Most commonly encountered in written English.
In order to expiate my guilt for the part I played in Tom being fired, I offered him some money to tide him over until he could find another job.
When the scandal broke, rather than deny it the public figure released a statement of expiation, accepting full responsibility and issuing a frank apology.
Expiatory measures were taken by the company to make amends for the environmental disaster that their mismanagement had caused.