Left one in a card with her name (5)
I believe the answer is:
alice
'her name' is the definition.
'left one in a card' is the wordplay.
'left' becomes 'l' (common abbreviation).
'one' becomes 'i' (Roman numeral).
'in' indicates putting letters inside.
'a card' becomes 'ace' (ace is a type of playing card).
'l'+'i'='li'
'li' going inside 'ace' is 'ALICE'.
'with' is the link.
(Other definitions for alice that I've seen before include "Lewis Carroll's heroine" , "Girl in literary Wonderland" , "Immortal girl in Wonderland" , "Wonderland girl's name" , "She fell down a rabbit hole into a fantasy world" .)