Retiring girl eating last of broccoli for fibre (5)
I believe the answer is:
sisal
'fibre' is the definition.
(sisal is a kind of fibre)
'retiring girl' is the wordplay.
'retiring' becomes 'si' (I can't justify this - if you can you should believe this answer much more).
'girl' becomes 'sal' (feminine given name).
'si'+'sal'='SISAL'
'eating last of broccoli for' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Other definitions for sisal that I've seen before include "Fibre used in rope-making" , "Fibre-yielding plant" , "Agave rope-fibre" , "Sails (anag) - fibre" , "Plant fibre used for making rope" .)