Happiness is a woman ... (3)
I believe the answer is:
joy
This clue is a double definition.
'happiness' is the first definition.
(I have seen 'Great happiness ' mean 'joy' so perhaps 'happiness' could also mean 'joy')
'woman' is the second definition.
'is a' acts as a link.
(Other definitions for joy that I've seen before include "Subject of 11 [ODE]" , "Rapture" , "Intense gladness" , "Great happiness" , "Delight" .)