One of the most important factors in a relationship is trust. True love always should include trust because the term denotes mostly all vital needs that could keep a relationship strong and healthy all throughout. Trust is something that will always keep you secure with your partner. In many circumstances, there are relationships that break up due to some misunderstandings like not being loyal to her or not fulfilling her perception of you.
It is always hard to gain her trust back but if you love her enough that you cannot live without her, making it a point to gain her trust back should be easy because true love cannot be apart for long. So many guys suffer a lot, especially when they are true and their love distrusts them.
The first thing that a guy could do is apologize for the mistake that he has committed but it still wouldn't be enough to gain her trust back. It will take some time but make sure it is obvious that you're making it a point to rectify yourself and are going to be a changed man. If you ex sees that you have changed it might help and then you might be able to start over again. It is very important that you make her feel that she just made the right choice by not moving on.
Love without trust is no love, if you love each other you should first create a bond of trust between each other and then start loving one another deeply.