A church covering up new outbreaks? (4)

I believe the answer is:

acne

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'a church covering up new outbreaks?' is the definition.
I can't judge whether this definition defines the answer.

'a church covering up new' is the wordplay.
'church' becomes 'CE' (abbreviation for Church of England).
'covering up' is an insertion indicator.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'ce' placed around 'n' is 'cne'.
'a'+'cne'='ACNE'

Can you help me to learn more?

(Other definitions for acne that I've seen before include "Adolescent skin disease" , "Teenage skin blemish" , "Adolescent spots" , "Skin complaint" , "Cane for the teenager?" .)

I've seen this clue in The Independent.

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