Cape songbird down by new university (5)
I believe the answer is:
fichu
'cape' is the definition.
(I've seen this before)
'songbird down by new university' is the wordplay.
'songbird' becomes 'finch' (I've seen this before).
'down by' is a deletion indicator (to be down something is to be lacking it).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'university' becomes 'u' (abbreviation for university).
'finch' with 'n' taken away is 'fich'.
'fich'+'u'='FICHU'
(Other definitions for fichu that I've seen before include "Lace shawl" , "Light triangular scarf" , "Cloth triangle" , "Eighteenth-century woman's light scarf" , "Triangular piece of muslin for the neck" .)