“You should definitely bring that up.”
You and a partner are preparing to give a presentation for a class you're taking. You're discussing the topic of your presentation, and your partner mentions some information she found while researching the topic. You think she should say something about that in the presentation. You tell her this.
You should definitely bring that up.
This means to introduce a topic into the conversation, or to start talking about a topic.
When you use "that", "it", "her" or other pronoun, the order is "bring ___ up". When you use a noun or longer phrase, use the order "bring up ___"
I'm glad you brought that up.
I don't know why she had to bring up the fact that we used to go out in front of all those people.
This is a way to suggest that a person do something. Although it's a very direct suggestion, it sounds polite and helpful:
You should definitely ask for a raise after all the extra time you've been putting in this year.