Work period cut one's minute hope (8)
I believe the answer is:
optimism
'hope' is the definition.
(optimism is a kind of hope)
'work period cut one's minute' is the wordplay.
'work' becomes 'op' (abbreviation for opus).
'period cut' becomes 'tim' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'one's' becomes 'is' (Roman numeral).
'minute' becomes 'm' (abbreviation).
'op'+'tim'+'is'+'m'='OPTIMISM'
Can you help me to learn more?
(Other definitions for optimism that I've seen before include "Mind-frame that looks on the bright side" , "Glass half-full attitude" , "Confident outlook" , "Looking on the bright side" , "Hopeful nature" .)