A cardinal holding island back? That's ludicrous (7)
I believe the answer is:
asinine
'that's ludicrous' is the definition.
(I've seen this in another clue)
'a cardinal holding island back?' is the wordplay.
'cardinal' becomes 'nine' (a cardinal number).
'holding' means one lot of letters goes inside another.
'island' becomes 'is' (abbreviation).
'back?' says the letters should be written backwards (I've seen 'backed' mean this).
'is' backwards is 'si'.
'a'+'nine'='anine'
'anine' placed around 'si' is 'ASININE'.
(Other definitions for asinine that I've seen before include "Daft" , "In the nature of supposedly stupid animal" , "Really silly, ridiculous" , "Absurd" , "Idiotic" .)