Sport is hard to run (4)

I believe the answer is:

rush

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'run' is the definition.
(I know that rush is a type of run)

'sport is hard' is the wordplay.
'sport' becomes 'rus' (I can't justify this - if you can you should believe this answer much more).
'is hard' becomes 'h' (abbreviation used in pencil classifications).
'rus'+'h'='RUSH'

'to' is the link.

Can you help me to learn more?

(Other definitions for rush that I've seen before include "Hurry - marsh plant" , "Charge" , "Traffic is busiest at this hour" , "Be too hasty or too fast" , "Marsh plant - fly" .)

I've seen this clue in The Times.

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