Wool supplier completely backed by mother (5)
I believe the answer is:
llama
'wool supplier' is the definition.
(I know that llama this taxon is source of llama fiber)
'completely backed by mother' is the wordplay.
'completely' becomes 'all' (synonyms).
'backed' is a reversal indicator.
'by' says to put letters next to each other.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'all' written backwards gives 'lla'.
'lla'+'ma'='LLAMA'
(Other definitions for llama that I've seen before include "As bearer of burdens" , "Peruvian beast of burden" , "South-American cud-chewing animal" , "South American animal like the camel" , "Domesticated pack animal of the Andes" .)