In reply to hatchleader:
Hmm... You begin by saying:
> and seems to be not fussed about going further.
And then, in a later post:
> She seems to want to improve
Crucially, you need to find out: which is it?
If she doesn't want to improve, you can climb inside and do sport routes outside forever and a day. My best times at sport were with my partner, who doesn't climb. We'd go for a walk and then have a couple of hours of me either doing mileage or pushing as hard as I could.
Your girlfriend can probably second you on trad as well (if she wants).
Alternatively, if she wants to get better, it's falling practice, bouldering, linking moves/sections, two grades: onsight and redpoint. Etc. Etc.
But you need to find out which it is...
Good luck.
Mick