How can I regain trust from my partner again?

Looking at the big picture, then I believe the best apology is changed behaviour. By changing your behaviour, you will be able to show your partner that you are truly sorry and regret whatever mistake you could have committed. This is how I would forgive my partner and how I would want to be forgiven. But it is definitely very individual. And how you will change your behaviour, is different. It depends on why that person lost their trust in you in the first place. It also depends on what kind of person your partner is/was, and how your relation to them is/was.