An idea, alas, or odd composition that’s very much late! (4,2,1,8)
I believe the answer is:
dead as a doornail
'very much late' is the definition.
(phrase meaning dead)
'an idea alas or odd composition' is the wordplay.
'composition' indicates an anagram.
'an'+'idea'+'alas'+'or'+'odd'='anideaalasorodd'
'anideaalasorodd' anagrammed gives 'DEAD AS A DOORNAIL'.
'that's' is the link.
(Other definitions for dead as a doornail that I've seen before include "just like a dodo!" , "far from quick!" , "Like one driven through entrance" .)