TS Eliot works about animal giving a lump in the throat (10)
I believe the answer is:
epiglottis
'a lump in the throat' is the definition.
(piece of cartilage in the throat)
'ts eliot works about animal' is the wordplay.
I cannot quite understand how this works, but
'works' could be 'is' ('be' can be a synonym of 'work') and 'is' is located in the answer.
'animal' could be 'pig' (I've seen this in other clues) and 'pig' is located in the answer.
This explanation may well be incorrect...
'giving' acts as a link.
(Other definitions for epiglottis that I've seen before include "Thin flap in the throat" , "stop for a breather" .)