Describing one-party system — attritional, beginning to age terribly (12)
I believe the answer is:
totalitarian
'describing one-party system' is the definition.
'attritional beginning to age terribly' is the wordplay.
'beginning to' says to take the initial letters.
'terribly' is an anagram indicator.
The first letter of 'age' is 'a'.
'attritional'+'a'='attritionala'
'attritionala' with letters rearranged gives 'TOTALITARIAN'.
(Other definitions for totalitarian that I've seen before include "Tyrannical" , "Of ultimate-State-control system" , "Despotic" , "Allowing no opposition" , "(Of states) extremely dictatorial" .)