Line part of suit in delicate fabric (4)

I believe the answer is:
lace
'delicate fabric' is the definition.
(I've seen this in another clue)
'line part of suit' is the wordplay.
'line' becomes 'l' (used when specifying particular lines from a poem).
'part of suit' becomes 'ace' (I can't justify this - if you can you should believe this answer much more).
'l'+'ace'='LACE'
'in' is the link.
Can you help me to learn more?
(Other definitions for lace that I've seen before include "Fine needlework" , "Delicate open-weave fabric" , "Fine open fabric" , "Famous play ''Arsenic and Old . . . .''" , "Shoestring: delicate ornamental fabric" .)