Ruin intro with hesitancy — it's no longer important! (7,7)
I believe the answer is:
ancient history
'it's no longer important' is the definition.
(phrase for something unimportant or forgotten)
'ruin intro with hesitancy' is the wordplay.
'ruin' is an anagram indicator.
'with' says to put letters next to each other.
'intro' put after 'hesitancy' is 'hesitancyintro'.
'hesitancyintro' anagrammed gives 'ANCIENT HISTORY'.
(Other definitions for ancient history that I've seen before include "something obtained from old documents?" , "The period of Greece and Rome" , "that happened long ago" , "accounts of Roman empire" , "There's something very familiar" .)