Build a green bridge over Leith Walk.
This would build a low traffic link connecting Pilrig Park and the traffic free path running east from Easter Road. More info at http://tinyurl.com/ld7kzu
Calum MacKellar commented
I understand the point but believe that this would be a very bad idea. It would make Leith Walk look like a tunnel. In the past there was a railway bridge over the Walk that made it look terrible (see old photos).
As an alternative may I propose a dedicated cycle crossing (like pedestrian crossing) over Leith Walk. This wouls be a lot better and not so ugly.