Crossword Genius

A nurse covering up daughter's conduct (10)

Ross

I believe the answer is:

administer

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'conduct' is the definition.
(I've seen this before)

'a nurse covering up daughter's' is the wordplay.
'nurse' becomes 'minister' (I can't explain this - if you can you should believe this answer much more).
'covering up' indicates putting letters inside.
'daughter' becomes 'd'.
'a'+'minister'='aminister'
'aminister' enclosing 'd' is 'ADMINISTER'.

Can you help me to learn more?

(Other definitions for administer that I've seen before include "give" , "Manage" , "man?" , "Dispense" , "Govern" .)

I've seen this clue in The Times.
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