Tube that is inverted in vivisection — extremely (4)
I believe the answer is:
vein
'tube' is the definition.
(I know that vein is a type of blood vessel)
'that is inverted in vivisection extremely' is the wordplay.
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'inverted' says the letters should be written in reverse.
'in' is an insertion indicator.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'vivisection' with its centre taken out is 'vn'.
'ie' written backwards gives 'ei'.
'ei' inserted inside 'vn' is 'VEIN'.
(Other definitions for vein that I've seen before include "Tube that carries blood to the heart" , "Vessel carrying blood towards the heart" , "Vessel for claret" , "part of a vital system" , "Irregular streak of colour" .)