Infallible authorities lose car that's ordered (7)
I believe the answer is:
oracles
'infallible authorities' is the definition.
(I've seen this in another clue)
'lose car that's ordered' is the wordplay.
'that's ordered' indicates anagramming the letters.
'lose'+'car'='losecar'
'losecar' with letters rearranged gives 'ORACLES'.
(Other definitions for oracles that I've seen before include "Solacer for wise or knowledgeable people" , "Places where ancient Greek consulted their gods" , "They were consulted by ancient Greeks" , "Prophets, seers" , "They would be asked questions" .)