Any birth mishandled after onset of labour is a perplexity (9)
I believe the answer is:
labyrinth
'a perplexity' is the definition.
'any birth mishandled after onset of labour' is the wordplay.
'mishandled' is an anagram indicator.
'after' means one lot of letters go next to another.
'onset of' says to take the initial letters.
The initial letter of 'labour' is 'l'.
'any'+'birth'='anybirth'
'anybirth' with letters rearranged gives 'abyrinth'.
'abyrinth' after 'l' is 'LABYRINTH'.
'is' is the link.
(Other definitions for labyrinth that I've seen before include "hard to get out of" , "Complex network of passages" , "Maze, tangled network" , "perplexity?" , "listening equipment" .)