Older lamb's family's fleece (9)
I believe the answer is:
sheepskin
'fleece' is the definition.
(I know that fleece can be written as sheepskin)
'older lamb's family's' is the wordplay.
'older lamb's' becomes 'sheep's'.
'family' becomes 'kin' (synonyms).
'sheeps'+'kin'='SHEEPSKIN'
(Other definitions for sheepskin that I've seen before include "leather" , "coat" , "Fleece garment" , "Ovine outer layer used in coats and rugs" , "Body covering of an ovine mammal" .)