Non-specific heredity factor, almost fertile (7)
I believe the answer is:
generic
'non-specific' is the definition.
(I've seen this before)
'heredity factor almost fertile' is the wordplay.
'heredity factor' becomes 'gene' (I've seen this in another clue).
'almost' means to remove the last letter (most of the word but not all of it).
'fertile' becomes 'rich' (synonyms).
'rich' with its last letter removed is 'ric'.
'gene'+'ric'='GENERIC'
(Other definitions for generic that I've seen before include "Common" , "Of a whole genus or group" , "appropriate for the whole class" , "Referring to a whole class or group" , "Applicable to a whole class or group" .)