Unbiased individual initially given role in distribution of mail (9)
I believe the answer is:
impartial
'unbiased' is the definition.
(similar in meaning)
'individual initially given role in distribution of mail' is the wordplay.
'initially' suggests taking the first letters.
'given' says to put letters next to each other.
'role' becomes 'part' (synonyms).
'in' means one lot of letters goes inside another.
'distribution of' indicates anagramming the letters.
The initial letter of 'individual' is 'i'.
'mail' with letters rearranged gives 'mial'.
'part' inserted within 'mial' is 'mpartial'.
'i'+'mpartial'='IMPARTIAL'
(Other definitions for impartial that I've seen before include "Showing lack of favouritism" , "Fair, unprejudiced" , "Disinterested" , "Unbiased" , "Treating all rivals equally" .)