Hereditary factor somewhat degenerate (4)
I believe the answer is:
gene
'hereditary factor' is the definition.
'somewhat degenerate' is the wordplay.
'somewhat' indicates a hidden word.
'GENE' can be found hidden inside 'degenerate'.
(Other definitions for gene that I've seen before include "-- Pitney, singer" , "Embarrassment" , "Factor controlling heredity carried by chromosome" , "Basic unit of heredity" , "Biological factor determining heredity" .)