Imponderable popular taste gets bile churning (10)
I believe the answer is:
intangible
'imponderable' is the definition.
(thesaurus)
'popular taste gets bile churning' is the wordplay.
'popular' becomes 'in'.
'taste' becomes 'tang' (tang is a kind of taste).
'gets' means one lot of letters go next to another.
'churning' is an anagram indicator.
'bile' with letters rearranged gives 'ible'.
'in'+'tang'+'ible'='INTANGIBLE'
(Other definitions for intangible that I've seen before include "Elusive" , "unclear" , "Abstract - hard to grasp" .)