First, it would be good to know why there is a lack of trust. Is it because one of the two partners has had an affair? Or, conversely, is it because one of the two partners suspects the other of having affairs, whether or not it's true? In any case, this lack of trust can lead to suspicion, lack of communication and a host of other unpleasantries.
Assuming that trust was there from the beginning, what can lead to a breakdown in this trust? Suspicious behavior by one or both of the partners is a certain sign.
If one of the two partners starts receiving communications (via phone, text or email) and shows a lack of desire to share what the communication was about, this will often lead to suspicion. What's the big secret? Whether the suspicion is founded or not almost becomes irrelevant. It's the fact that one chooses not to share that leads to the suspicion. And suspicion almost always leads to some breakdown in trust.
The best way to avoid a lack of trust is to communicate effectively. It's probably a good idea to include your partner in things that interest you. This doesn't mean that the two of you have to do everything together all the time. But sharing your interests with each other makes both of your interests more enjoyable. It really isn't too much to ask that you include your partner-if only in the sense of telling him/her why and how your interests are of interest to you.