Kate managed to eat nearly every bun
I believe the answer is:
teacake
'bun' is the definition.
(I've seen this before)
'kate managed to eat nearly every' is the wordplay.
'managed' indicates an anagram.
'to eat' means one lot of letters goes inside another.
'nearly' means to remove the last letter.
'every' becomes 'each' (synonyms).
'kate' is an anagram of 'take'.
'each' with its final letter taken off is 'eac'.
'take' placed around 'eac' is 'TEACAKE'.
(Other definitions for teacake that I've seen before include "Scones with raisins, toasted and buttered" , "Bun for toasting" , "Bun served toasted" , "Sweet thing" , "(Afternoon) bun" .)