Covering handy game (5)

I believe the answer is:

rugby

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'game' is the definition.
(rugby is a sport or game)

'covering handy' is the wordplay.
'covering' becomes 'rug' (rug is a kind of covering).
'handy' becomes 'by' (I can't justify this - if you can you should believe this answer much more).
'rug'+'by'='RUGBY'

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(Other definitions for rugby that I've seen before include "Game; town" , "Game named after school" , "The 13-a-side game" , "Famous public school" , "Public school - sport" .)

I've seen this clue in the Sydney Morning Herald.

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