Strike reduced doctor's rise (5)

I believe the answer is:

climb

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'rise' is the definition.
(I know that rise can be written as climb)

'strike reduced doctor's' is the wordplay.
'strike' becomes 'cli' (I can't explain this - if you can you should believe this answer much more).
'reduced' means to remove the last letter.
'doctor's' becomes 'MB's' (Bachelor of Medicine, Medicinae Baccalaureus).
'mbs' with its last letter taken off is 'mb'.
'cli'+'mb'='CLIMB'

Can you help me to learn more?

(Other definitions for climb that I've seen before include "Ascend, escalate" , "improve one's social status" , "Scale or clamber" , "Get a rise" , "Slope upwards" .)

I've seen this clue in The Telegraph.

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