Since Cole has been advocating that Ariadne come and chill with Leliana, she'll be interested to see what she can do and how she handles herself on a mission. She'd probably send a letter and ask Ariadne to come and speak with her in person if she wanted to participate in a mission, but we can hammer out details when we thread it :]b

She probably wouldn't have any special assignments or instructions for Ariadne since it's their first time working together but she be interested in knowing her thoughts after, and such.