Rice possibly is upset with the heads of Dubya’s executive organisation (4,5)

'rice possibly' is the definition.
(rice is an example)

'is upset with the heads of dubya's executive organisation' is the wordplay.
'upset with' indicates an anagram.
'the heads of' says to take the initial letters.
'organisation' becomes 'order' (order is a kind of organization).
The first letters of 'dubya executive' is 'de'.
'is' anagrammed with 'de' can make 'side'.
'side'+'order'='SIDE ORDER'