There is no way that gives 100 percentage accuracy on how to find out whether a partner is loyal or not.
Nevertheless, there are a few ways to gather some information if a partner is loyal or not.
Changes in habits, is a way to go about this, did you have access to your partner's devices in the past and now you don't? Does your partner tell you about all the friends and new friends they had in the past but now he/she doesn't? Is your partner being too careful around you?
If you answered yes to all the questions above you can try to put your partner to a test. Observe your partner's movements, you can hire someone to do this for you or you can set your partner up with an opposite sex.
Be careful how you go about finding if your partner is loyal or not so you don't complicate the whole thing and get into trouble.
There is no sure app for doing so. However, you can infer from different habits of your spouse. Whether he lets you use his phone or not, whether he is free about talking about all of his friends. You can also put him to certain tests. Hire a girl to try to pick him up or ask your friend to do so.
Another way is to follow him around secretly and observe his daily interactions. If you really want to find out what he is up to, you can download certain hacks or employ a professional hacker to find what is going on in his phone.