In favour of celebrated singer doing it for nothing (3,4)

I believe the answer is:

pro bono

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'doing it for nothing' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'in favour of celebrated singer' is the wordplay.
'in favour of' becomes 'pro' (being pro a particular cause).
'celebrated singer' becomes 'bono' (singer from U2. I am not sure about the 'celebrated' bit.).
'pro'+'bono'='PRO BONO'

Can you help me to learn more?

(Other definitions for pro bono that I've seen before include "-- -- publico (Latin)" , "Giving free services" , "with no charges" , "Done for the public good unpaid" , "not being paid" .)

I've seen this clue in The Irish Times.

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