What one would expect from the flying padre? (3,7)

I believe the answer is:

air service

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'flying padre?' is the definition.
'air service' can be an answer for 'flying' (thesaurus). I am not certain of the 'padre?' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

I've seen this clue in The Irish Independent.

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