A fairly normal district (6)
I believe the answer is:
parish
'a fairly normal district' is the definition.
'parish' can be an answer for 'district' (parish is a kind of district). I am not sure about the 'a fairly normal' bit.
'normal district' is the wordplay.
'normal' becomes 'par' (as in par for the course).
'district' becomes 'ish' (I am not sure about this - if you are sure you should believe this answer much more).
'par'+'ish'='PARISH'
Can you help me to learn more?
(Other definitions for parish that I've seen before include "Unit of local government" , "area known to clergyman" , "Ecclesiastical district" , "District within county" , "District with own church and clergyman" .)