Lack of fairness some strain, I quit yesterday (8)
I believe the answer is:
iniquity
'lack of fairness' is the definition.
(iniquity is wickedness or cruelty)
'some strain i quit yesterday' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'INIQUITY' can be found hidden inside 'strain i quit yesterday'.
(Other definitions for iniquity that I've seen before include "Gross injustice; crime" , "Great wickedness or injustice" , "Heinousness" , "immorality" , "Going wrong" .)