Arranging birth holding baby's head (7)

I believe the answer is:

combing

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'arranging' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'birth holding baby's head' is the wordplay.
'birth' becomes 'coming' (I can't justify this - if you can you should believe this answer much more).
'holding' is an insertion indicator.
'head' suggests taking the first letters.
The initial letter of 'babys' is 'b'.
'coming' going around 'b' is 'COMBING'.

Can you help me to learn more?

(Other definitions for combing that I've seen before include "groom's role?" , "Systematically examining" .)

I've seen this clue in The Telegraph.

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