She has a line in fancy lace (5)
I believe the answer is:
celia
'she' is the definition.
'a line in fancy lace' is the wordplay.
'a line' becomes 'i' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' is an insertion indicator.
'fancy' indicates an anagram.
'lace' with letters rearranged gives 'cela'.
'i' put into 'cela' is 'CELIA'.
'has' is the link.
Can you help me to learn more?
(Other definitions for celia that I've seen before include "Daughter to Frederick" , "Frederick's daughter" , "lady" , "Character in Tales from Shakespeare" , "Rosalind's cousin" .)