Live and prosper without love (5)
I believe the answer is:
dwell
'live' is the definition.
('dwell' can be a synonym of 'live')
'prosper without love' is the wordplay.
'prosper' becomes 'dowell'.
'without' indicates named letters should be taken away.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'dowell' with 'o' removed is 'DWELL'.
'and' is the link.
(Other definitions for dwell that I've seen before include "Lodge" , "Inhabit" , "Live (in a place)" , "Hang out" , "Harp" .)