Padre upset about Charlie being Military Police (6)

I believe the answer is:

redcap

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'military police' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'padre upset about charlie' is the wordplay.
'upset' is an anagram indicator.
'about' is an insertion indicator.
'charlie' becomes 'c' (phonetic alphabet: alpha, bravo, charlie etc.).
'padre' anagrammed gives 'redap'.
'redap' going around 'c' is 'REDCAP'.

'being' is the link.

Can you help me to learn more?

(Other definitions for redcap that I've seen before include "MP" , "bird!" , "Member of the military police" , "Hole from explosion" , "Goldfinch" .)

I've seen this clue in the Evening Standard.

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