I believe that theres more than just trust. Without comunication you cant have trust, and without trust you cant have a relationship.
Relationship is built with two people on a stable ground. This ground is trust and comunication. If something goes missing or breaks, the whole pyramid falls leaving you confussed and broken about why it failed.
So yes, it is very important to feel able to trust your partner with yourself. Cause you are opening up to them, and trust, to not break you. Also trust makes you feel secure too.
You cant have a relationship with someone, that you know, would stick a knife to your back or even worst to your front… and live with it. It would be unhealthy and depressing. But you can like them. That’s another thing…
so i hope i answered your question as best as i could!!