Exist over a long period (3)
I believe the answer is:
era
'a long period' is the definition.
(I've seen this before)
'exist over' is the wordplay.
'exist' becomes 'are' ('they exist' means 'they are').
'over' shows that the letters should be reversed in order.
'are' in reverse letter order is 'ERA'.
(Other definitions for era that I've seen before include "Aeon" , "Important date" , "Important time" , "Epoch, period" , "8" .)