Repeated time and time again in new diet (8)

I believe the answer is:

iterated

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'repeated' is the definition.
('iterate' can be a synonym of 'repeat')

'time and time again in new diet' is the wordplay.
'time and time again' becomes 'rate' (I can't explain this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'new' is an anagram indicator.
'diet' anagrammed gives 'ited'.
'rate' placed into 'ited' is 'ITERATED'.

Can you help me to learn more?

(Other definitions for iterated that I've seen before include "Done over" , "Kept repeating" , "Repeated or stated repeatedly" , "Said or did again" , "given repeat" .)

I've seen this clue in The Guardian.

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