Survive with bit of cereal (4)
I believe the answer is:
wear
'survive' is the definition.
(thesaurus)
'with bit of cereal' is the wordplay.
'with' becomes 'w' (short for with).
'bit of cereal' becomes 'ear' (as in an ear of wheat or another cereal grain).
'w'+'ear'='WEAR'
(Other definitions for wear that I've seen before include "Tolerate" , "Have on the body as clothes or ornaments" , "Become tiresome" , "Clothes; chafe" , "Northern river - sport" .)