On entering the north-east, nil (4)
I believe the answer is:
none
'nil' is the definition.
(I've seen this in another clue)
'on entering the north-east' is the wordplay.
'entering' means one lot of letters goes inside another.
'the north east' becomes 'ne'.
'on' going into 'ne' is 'NONE'.
(Other definitions for none that I've seen before include "Bugger all" , "0?" , "Not any sort of neon" , "What's left after taking all" , "Zero" .)