A poo gushes out from this part of the digestive system (10)
I believe the answer is:
oesophagus
'this part of the digestive system' is the definition.
('oesophagus' is part of 'digestive system')
'a poo gushes out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'a'+'poo'+'gushes'='apoogushes'
'apoogushes' with letters rearranged gives 'OESOPHAGUS'.
'from' is the link.
(Other definitions for oesophagus that I've seen before include "Gullet" , "Throat to stomach link" .)