Generated out of love, but unhappy (5)
I believe the answer is:
bored
'unhappy' is the definition.
(thesaurus)
'generated out of love' is the wordplay.
'generated' becomes 'bred' (I've seen this before).
'out of' is an insertion indicator (some letters on the outside of others).
'love' becomes 'o' (love means zero in tennis).
'bred' placed around 'o' is 'BORED'.
'but' is the link.
(Other definitions for bored that I've seen before include "Wearied by tedium" , "Brassed off" , "Fed up, afflicted with ennui" , "Used drill on" , "Filled with ennui" .)