Lead potentially has eider and gannet suffering (11)
I believe the answer is:
tragedienne
'lead potentially' is the definition.
'eider and gannet suffering' is the wordplay.
'and' says to put letters next to each other.
'suffering' is an anagram indicator.
'eider'+'gannet'='eidergannet'
'eidergannet' with letters rearranged gives 'TRAGEDIENNE'.
'has' acts as a link.
(Other definitions for tragedienne that I've seen before include "Female dramatic actress" , "Performer" , "Serious actress" , "Sort of actress" .)