Period leading to inevitable extinction (7)
I believe the answer is:
erasure
'extinction' is the definition.
(thesaurus)
'period leading to inevitable' is the wordplay.
'period' becomes 'era' (era is a kind of period).
'leading to' says to put letters next to each other (some letters go before or lead others).
'inevitable' becomes 'sure' (similar in meaning).
'era'+'sure'='ERASURE'
(Other definitions for erasure that I've seen before include "clearing of tape" , "Band with Andy Bell and Vince Clarke, or wipe-out" , "group from the 80s" , "Wiping out - English pop duo" , "Rubbing out - English synthpop duo" .)