Great man to run out! (5)

I believe the answer is:

peter

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'out' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'great man to run' is the wordplay.
'great man' becomes 'pete' (I am not sure about the 'great' bit.).
'to run' becomes 'r' (cricket abbreviation).
'pete'+'r'='PETER'

Can you help me to learn more?

(Other definitions for peter that I've seen before include "Blue -, ship's flag" , "Dwindle away to nothing" , "Boy's name - safe" , "prison cell" , "-- Sellers, comic actor" .)

I've seen this clue in the Evening Standard.

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