Scottish have a standing agreement with Edinburgh which specifies that arrivals should be spaced a minimum of 8nm in trail, at 250 knots and level at Minimum Stack Level (roughly the Flight Level Equivalent of 7000ft QNH) by TARTN.
The level restriction ensures that you can slow down further for sequencing purposes (210 knots etc) but still have sufficient track miles to join the ILS Glidepath at 10 miles.
It also allows both Edinburgh and Scottish the option to place arrivals in the TWEED hold if traffic congestion becomes a problem. Without the level restriction arrivals would join the hold at higher levels, which causes difficulty in stacking subsequent arrivals.
If Edinburgh give you descent on contact below the Min Stack Level, you are quite correct in saying that the TARTN restriction no longer applies, unless it is restated in the descent instruction. However, your descent profile will already be established in the desired envelope, so this does not present a problem.
During quiet periods controllers may omit the TARTN level restriction, when it is clear that holding or late speed reductions will be not be necessary.
Hope this is useful.