Repeat the thing time after time - to the end of time! (7)
I believe the answer is:
iterate
'repeat' is the definition.
('iterate' can be a synonym of 'repeat')
'the thing time after time to the end of time' is the wordplay.
'the thing' becomes 'it'.
'time' becomes 'era' (I've seen this before**).
'after' says to put letters next to each other.
'time' becomes 't'.
'to the end of' indicates one should take the final letters.
The final letter of 'time' is 'e'.
'it'+'era'+'t'+'e'='ITERATE'
(Other definitions for iterate that I've seen before include "Recapitulate" , "Utter or perform repeatedly" , "Say again, repeat" , "State repeatedly, say again" , "Repeat, state again" .)