Fat left a stain finally on jazzy lino (7)
I believe the answer is:
lanolin
'fat' is the definition.
(thesaurus)
'left a stain finally on jazzy lino' is the wordplay.
'left' becomes 'l' (common abbreviation**).
'finally' says to take the final letters.
'on' is an insertion indicator (as in clothing \'on\' a person).
'jazzy' indicates anagramming the letters.
The last letter of 'stain' is 'n'.
'a'+'n'='an'
'lino' with letters rearranged gives 'noli'.
'an' enclosing 'noli' is 'anolin'.
'l'+'anolin'='LANOLIN'
(Other definitions for lanolin that I've seen before include "Oil extracted from wool" , "substance found in ointments" , "Oily substance on wool" , "Fatty coating on wool" , "Wool fat used in ointments" .)