Partiality shown by relocating postmen across island (8)
I believe the answer is:
nepotism
'partiality' is the definition.
(I've seen this before)
'relocating postmen across island' is the wordplay.
'relocating' indicates an anagram (I've seen 'relocated' mean this).
'across' means one lot of letters goes inside another.
'island' becomes 'i' (geographical abbreviation).
'postmen' anagrammed gives 'nepotsm'.
'nepotsm' going around 'i' is 'NEPOTISM'.
'shown by' is the link.
(Other definitions for nepotism that I've seen before include "Jobs for the boys" , "Favouritism shown in hiring relatives" , "The practice of favouring one's relatives in making official appointments" , "Fixing up the relatives with good jobs" , "Undue partiality" .)