I don't think that there would be anything wrong with pursuing your feelings. This based purely on the fact that she shows interest in you as well and that her current partner seems to acknowledge the fact that she is still into you. Perhaps he is even expecting you to make a (successful) move on her any time soon.
The problem i have with your original post is that you want to "ask" her to try again. While this is something to be considered since your feelings seem to be mutual, i would advise against it because it gives on of the two exes an "upper hand". The status quo should always be maintained when it comes to power-balance.
Finally, if she is into you, and you obviously are into her as well, what are you waiting for? If you don't try you will never know. 4 years isn't a short period of time and even if it was you both had your cool-off period and still want eachother. There is no harm in that.
The first step to fixing broken relationships is to accept that they have ended - getyourextowantyouback.org