Old writer not keeping any secrets (4)

I believe the answer is:

open

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'not keeping any secrets' is the definition.
I can't tell whether this definition defines the answer.

'old writer' is the wordplay.
'old' becomes 'o' (abbreviation).
'writer' becomes 'pen' (something which writes).
'o'+'pen'='OPEN'

Can you help me to learn more?

(Other definitions for open that I've seen before include "sporting competition" , "Exposed; free" , "Undo; exposed to attack" , "Unfasten" , "Frank and unlocked" .)

I've seen this clue in The Times.

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