Unpopular time for power cut (6)
I believe the answer is:
outage
'power cut' is the definition.
(an outage is a loss of power)
'unpopular time' is the wordplay.
'unpopular' becomes 'out' (similar in meaning).
'time' becomes 'age' (an age is a period of time).
'out'+'age'='OUTAGE'
'for' acts as a link.
(Other definitions for outage that I've seen before include "Power cut" , "Temporary suspension of operation" , "Emaciated" , "time of no power" , "loss of power" .)