Trust is a funny thing. Before you screw up you are given a bucket of it, gratis. It's like the handful of money you get at the beginning of a Monopoly game. The default, at least in the U.S. is to trust someone until they give a reason to distrust them.
That's nice, but after a screw-up, and especially after something as serious as drugs, it's very difficult to reestablish trust.
Two kinds of trust
Trust is about expectations. The two we have to reconstruct from the ashes are trust we have in ourselves and trust given by others. Both take time and I don't think either is ever completely made whole.
Coming to trust and believe in yourself is a step toward handling addiction that happens internally. We get a good look at our own human failings and learn to observe our behaviors with a critical eye. With time, we start to trust ourselves because we confront those inner cravings and don't act on them. If we mess up, we can take heart in restarting with a new appreciation of what we are up against and rejoin the battle. Every slip-up can help the process because we survive it and try again. Eventually, we come to trust our own ability to avoid the traps.
The problem with reestablishing trust in other relationships is that these inner struggles (both the victories and the temporary setbacks) aren't visible to others. They can't read our minds. What's worse, it's likely we've been lying to them for some time, and at least partly getting away with it. So I think this second sort of trust is harder and takes more than just time.
Sacrificing to get trust
By sacrifice here, I mean giving up some of those things which you trust yourself with (being able to see inside your own head) but others may not.
For instance, finances and money usually feed into every addiction. Whether it's shopping addiction or buying drugs, there is a money element that funds the habit. Exposing your finances and giving control to another says, "I know you don't trust me, so I'm willing to become completely transparent with money."
Another area is privacy. Every addiction has an element of sneaking around. You want to give this up as well. That could mean having a key-logger on your computer or not locking the bathroom door. Any way you can expose the "new you" to someone else will help build trust.
Sometimes you have to push. Your significant other might feel in impolite or intrusive to "check up" on your behavior. You'll need to explain why it's important.
Start by sharing all the devious things you once did to aid your habit. Teach them your tricks. Then, explain that by keeping an eye on you, they are actually helping you to stay on the straight and narrow by removing opportunity. Someone who cares about you will agree.
These are just some of the ways you can help build up trust again. Will it ever get to that pristine state from "before"? Maybe not. But, with time, it will get as good as it can be.