I think this is a bug with the new year 8 options that they're testing out. In the past you used to get the exclusive quest automatically when you reached level 7.
They're apparently testing out a feature that lets you pause exclusivity, but it's not properly implemented yet. Hopefully they'll fix it when year 8 comes out in a couple of days.
The only thing that we can do at the moment is wait until JC fix the "bug".
On my character, which is already in a romance, there used to be a button to break up with the person. Now that's been replaced with a button to pause the relationship. I think that these are new features for year 8 that they are testing out.
Hopefully when year 8 comes out tomorrow the bug will be fixed and you'll be able to get the exclusivity quest.