Trusting people is hard to do... and telling a nontrusting person to trust someone- is like throwing a shy person into a big room and saying don't be shy - trust comes over time... trust is earned... and sounds like you are on your way to doing that... consistency in a person is what earns my trust... that and just acknowledging me.
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Just relating my past experience here. The only time I wasn't in a happy and secure relationship was when I couldn't trust my ex bf. He was a complete flirt and it seemed to bother me a lot as he preferred an open relationship. To him, seeing and dating other people on a regular basis was perfectly normal. I wasn't possesive or anything like that and I did meet up with old friends once in a while myself. However, I just could not understand why he would rather see other women (regularly I mean) as I only met up with close friends during the time that we were together. Boy, my instincts proved right when he eventually cheated.
The main thing you should aim for now is to gain her trust. Well, perhaps you should try to make her feel that she is the only woman for you. Show her that she is first above all the others. Try spending more time with her doing things together. When she starts trusting you, she'll probably know that you won't leave her and with hopes, emotionally secure that you will always be there for her
That's what I think. If only there was trust in my previous year long relationship, things would have been much better. I felt that my ex did not put in much effort and I on the other hand was giving in too much.
Hope this piece of advice comes in handy as it actually happened to me before
What is the significance of a relationship without trust? Earn her trust and everything will work out well I hope. Good luck!