Here's the truth about respect in any relationship: If they do not respect you, they will never be loyal to you. If they physically or verbally abuse you, they do not respect you. If they neglect you, if they often ignore your texts and calls, if they makes excuses to not spend time with you, they do not respect you.
If they still hang out with an ex or flirt with others behind your back, they do not respect you. Forget about trust or honesty being first in a relationship. It needs to all start with respect. Because when you respect a partner, and in turn the relationship, you don't do dishonest things, you don't do things that betray trust, you don't exhibit shady behavior. If you are with someone who doesn't respect you, don't be a fool and stay with them because they will never be loyal to you.