The new development (Urbane Den. Or Urban Eden, whatever) sits in a triangle of land that was previously railway sidings etc. As Chdot says, there is still a line in daily use between Piershill Junction and Powderhall for the bin trains.
The triangle was bounded by railways on all sides until fairly recently, trains coming from Waverley would turn off at Abbeyhill Junction, run under London Road and through Abbeyhill Station at which point they could either take the left fork and head for Powderhall and on to Leith or take the right fork and head for Piershill and the East Coast Main Line. Slightly longer back, they could also continue straight on for Leith Central, crossing the current railway line on a bridge in the approximate location of the current road bridge behind Sainsburys (the one that has been closed off for so long). A lot of the new "Lochend Butterfly" housing is built on the infilled cutting of the lines to Leith Central. There was a further line connecting Leith Central to Piershill that followed the south boundary wall of Lochend Park.
There was an intention to build some turnback sidings on the trackbed at old Abbeyhill Station, but this was cancelled after EGIP was downgraded by Keith "Two More Lanes" Brown, after the trackbed was cleared and groundwork had been done.
There's lots of scope for excellent extentions of the NEPN once the Powderhall line is closed and (perhaps) lifted. Leith Walk, Easter Road, Meadowbank would all get traffic-free, grade separated connections to the NEPN.
I wonder if folks here are more in favour of the trackbeds being converted to foot/cycle ways or reserved for a long term aspiration to reinstate railway at Abbeyhill (difficult given the station was largely obliterated in recent years?)