Vetra Nyx is the third companion to join your party, as well as the third character you can romance with. She is a bisexual character - you can romance with her both with Sara and Scott Ryder. Vetra Nyx is a character you can have close relations with - by engaging in that relationship you won't be able to flirt and romance with other characters.
Note - before engaging in a close relationship you can save the game. Afterwards, you can go through the rest of the romance, load the saved game and engage into a relationship with a completely different character. The option to romance other characters is locked only when you are engaged in a close relationship with somebody.
Below you can find a table presenting all of Vetra's loyalty missions, coupled with the requirements that must be met to unlock them. Detailed description of every single one of them can be found in "Allies and relationships" section of this guide.
How to unlock
Vetra Nyx: Means and Ends
After returning from Kadara.
Vetra Nyx: A Moment Planetside
Complete "Vetra Nyx: Means and Ends" loyalty mission.
Note: the option to engage in a close relationship will appear during "Vetra Nyx: Means and Ends" loyalty mission. Remember that this choice will prevent you from flirting and romancing other characters. If you still want to romance with others and at the same time see the final parts the romance with Vetra, save the game before starting "Vetra Nyx: Means and Ends" mission and load it later if needed.