Appear to notice favouritism, finally (4)
I believe the answer is:
seem
'appear' is the definition.
('seem' can be a synonym of 'appear')
'notice favouritism finally' is the wordplay.
'notice' becomes 'see' (I've seen this before).
'finally' says to take the final letters.
The last letter of 'favouritism' is 'm'.
'see'+'m'='SEEM'
'to' acts as a link.
(Other definitions for seem that I've seen before include "Appear, give impression of being" , "Appear to the eye" , "Appear, look" , "Come across as" .)