Story on X about Conservative grasping organ (8)
I believe the answer is:
tentacle
'grasping organ' is the definition.
(I've seen this before)
'story on x about conservative' is the wordplay.
'story' becomes 'tale' (synonyms).
'on' means one lot of letters go next to another.
'x' becomes 'ten' (X is the Roman numeral for ten).
'about' is an insertion indicator.
'conservative' becomes 'C' (UK political abbreviation).
'tale' put after 'ten' is 'tentale'.
'tentale' going around 'c' is 'TENTACLE'.
(Other definitions for tentacle that I've seen before include "Octopus's "arm"" , "flexible arm?" , "Octopus feeler" , "Flexible feeling organ" , "Flexible grasping organ" .)