You have to be that partner who trusts and can be trusted, too.
It is presupposed that you are willing to trust them with your secrets and that they'd be willing to do the same.
You see, the thing about trust is that it grows. No one expects you to lay yourself bare before someone before the relationship reaches anywhere significant, but the willingness to do so has to always be present.
If you are thinking of entering into a relationship with someone and you are seeing signs that they can't be trusted with secrets, it is better to not even enter into a relationship with them at all.
It is not advisable to be with someone you can't fearlessly pour out all your fears, worries, dreams, and visions to. You need someone with whom your secrets are safe even if the relationship later hits the rocks.
And most importantly, you have to be that partner who trusts and can be trusted, too.
And to keep your partner's trust in you is just as easy as doing to them what you would have them do to you.
Being judgemental makes it difficult for your partner to comfortably tell you everything. Always try to keep an open mind.
Whether they are trying to introduce new activities into the relationship or giving you gist of mistakes they made, you need to be open-minded at all times.
If you must criticise for a wrong action, keep it as reasonable as possible. Hurtful words can be apologised for, not taken back.
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It is better to get people to talk to you when you open up to them.
If you are open with your fears, worries, visions, dreams and all that, it'll be easy for your partner to confide their deepest secrets in you, too.
There is such thing as privileged information and everything you hear or share in a relationship has that status.
Even if that relationship fails, treat those information as highly classified.
Don't hesitate to offer assistance. Their first point of call has to always be you and your willingness to help will keep this so.