Influential name is working with the terminally ill (7)
I believe the answer is:
seminal
'influential' is the definition.
(seminal can mean important or influential)
'name is working with the terminally ill' is the wordplay.
'working with' indicates anagramming the letters (working with the letters).
'the terminally ill' becomes 'l' (I can't explain this - if you can you should believe this answer much more).
'name'+'is'='nameis'
'nameis' anagrammed gives 'semina'.
'semina'+'l'='SEMINAL'
Can you help me to learn more?
(Other definitions for seminal that I've seen before include "Major" , "Highly original" , "Majorly influential" , "Menials (anag) - creative" , "Giving rise to new developments by menials" .)