Attempt to grab a small cigarette end? That's not fair! (6)
I believe the answer is:
biased
'not fair' is the definition.
(I've seen this in another clue)
'attempt to grab a small cigarette end?' is the wordplay.
'attempt' becomes 'bid' (bid is a kind of attempt).
'to grab' means one lot of letters goes inside another.
'small' becomes 's' (abbreviation - e.g. clothes size).
'end?' indicates one should take the final letters (I've seen 'end of' mean this).
The last letter of 'cigarette' is 'e'.
'a'+'s'+'e'='ase'
'bid' going around 'ase' is 'BIASED'.
'that's' is the link.
(Other definitions for biased that I've seen before include "'One-sided, slanted (6)'" , "Influenced unfairly" , "Having prejudice" , "not fair" , "Having favourite" .)