Crossword Genius

Don't attach much importance to power — give up (4,4)

Ross

I believe the answer is:

play down

I'm a little stuck... Click here to teach me more about this clue!

'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?" .)

I've seen this clue in The Guardian.
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