Irrational, being behind old governor (6)
I believe the answer is:
pilate
'governor' is the definition.
(Pontius Pilate, Roman governor in Christ's time)
'irrational being behind old' is the wordplay.
'irrational' becomes 'pi' (an irrational number).
'being behind' is a charade indicator (letters next to each other).
'old' becomes 'late' (I've seen this in other clues).
'pi'+'late'='PILATE'
(Other definitions for pilate that I've seen before include "Pontius -, Roman procurator of Judaea" , "Biblical Roman procurator of Judaea" , "famous old judge" , "Pontius, hand-washing judge" , "Biblical judge who asked 'What is truth'" .)