Some may say that trust builds over time, and that's true. But there are ways to make it easier for someone to trust you.
Suspicious partners often act in certain ways that their partner finds uncomfortable and invasive. Wanting to know where she's been, who she's been talking to, who she's been texting. Then she often tries to make him feel guilty for not simply trusting her, like he's supposed to trust her implicitly for no good reason. That sort of thing can be very damaging to the relationship. And often times the reason she's so sensitive about having to justify herself is because she really is cheating on him.
Most people will say that she is the one in the right, and that partners do need to simply trust each other and not worry when they're out with friends or even a single friend of the opposite sex and that they don't need to know where they've been or with whom. Well it's true that trust is important, but respect is also important, and it's more respectful to make it easier for your partner to trust you than to make it harder by expecting or demanding implicit automatic trust.
Anyway, the point of all this is that you can make it easier for someone to trust you by volunteering the sort of information a suspicious partner would ask for. Just straight up tell him who you've been talking to and who you've been with and where you've been etc. Casually offer evidence when convenient. This may feel like a little much, and nobody likes to feel judged or under suspicion and providing these things can perhaps imply to yourself that you're not trusted. But it can go a long way, and maybe it'll sink in after a while and he'll tell you that you don't need to do it anymore.
But whether you think that trust should be automatic or earned, it's safe to say that communication is always important. Make sure you keep talking to each other about your feelings. Make it clear how much you love him.