Name of female climber (3)
I believe the answer is:
ivy
This clue is a triple definition!
'name' is the first definition.
(woman's name)
'of' acts as a link.
'female' is the second definition.
(I've seen this before)
'climber' is the third definition.
(ivy is a climbing plant)
(Other definitions for ivy that I've seen before include "Old World vine" , "Clinging vine" , "Clinging evergreen" , "Hedera helix" , "Song: 'Poison --'" .)