Part of nose mum's unbandaged after a month (6)
I believe the answer is:
septum
'part' is the definition.
(septum is a kind of part)
'of nose mum's unbandaged after a month' is the wordplay.
'of' indicates an anagram (the answer comes from or 'of' the letters).
'nose' suggests taking the first letters (I've seen 'nose of' mean this).
'after' is a charade indicator (letters next to each other).
'a month' becomes 'sept' (Sept is an example).
The initial letters of 'mums unbandaged' is 'mu'.
'mu' is an anagram of 'um'.
'um' after 'sept' is 'SEPTUM'.
(Other definitions for septum that I've seen before include "Partition in nose between nostrils" , "Division between nostrils" , "Partition between two cavities of the nose" , "Partition between two chambers" , "Dividing partition between the nostrils" .)