Don't attach much importance to power — give up (4,4)
I believe the answer is:
play down
'don't attach much importance to power' is the definition.
I can't tell whether this definition defines the answer.
'give up' is the wordplay.
'give' becomes 'play' (I've seen this in another clue).
'up' becomes 'down' (I can't explain this - if you can you should give a lot more credence to this answer).
'play'+'down'='PLAY DOWN'
Can you help me to learn more?
(Other definitions for play down that I've seen before include "Give little importance to" , "Make light of" , "Minimise the importance of (something)" , "Understate the importance" , "what Antrim team may do?" .)