The old man repeatedly left in Vatican office? (5)

I believe the answer is:

papal

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'the old man repeatedly left in vatican office?' is the definition.
I can't judge whether this definition defines the answer.

'the old man repeatedly left' is the wordplay.
'the old man' becomes 'pa' (both can mean father).
'repeatedly' says to double the letters.
'left' becomes 'l' (common abbreviation).
'pa' duplicated is 'papa'.
'papa'+'l'='PAPAL'

Can you help me to learn more?

(Other definitions for papal that I've seen before include "Relating to the Pontiff" , "Like some bulls" , "of Catholic high-up" , "Of the highest Vatican authority" , "Relating to the Pope" .)

I've seen this clue in The Times.

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