Period of years formerly heading off decline (9)
I believe the answer is:
decadence
'decline' is the definition.
(I know that decline can be written as decadence)
'period of years formerly heading off' is the wordplay.
'period of years' becomes 'decade' (I've seen this before).
'formerly' becomes 'once' (synonyms).
'heading off' means to remove the first letter.
'once' with its initial letter taken off is 'nce'.
'decade'+'nce'='DECADENCE'
(Other definitions for decadence that I've seen before include "Immoral behaviour" , "Moral or cultural decline" , "Progressive decline" , "Degeneration" , "depravity" .)