Cooked limes used principally for breakfast cereal (6)
I believe the answer is:
muesli
'breakfast cereal' is the definition.
(I've seen this before)
'cooked limes used principally' is the wordplay.
'cooked' indicates anagramming the letters.
'principally' indicates taking the first letters.
The first letter of 'used' is 'u'.
'limes'+'u'='limesu'
'limesu' is an anagram of 'MUESLI'.
'for' acts as a link.
(Other definitions for muesli that I've seen before include "Rolled oats, nuts and fruit mixture" , "Mixture of crushed grain, nuts etc" , "Cereal made with oats and nuts" , "Breakfast mixture of dry cereals and fruits" , "Breakfast mix of oats, nuts, fruit etc" .)