Want to eliminate Republican loss (5)
I believe the answer is:
death
'loss' is the definition.
(I have seen 'Loss of life ' mean 'death' so perhaps 'loss' could also mean 'death')
'want to eliminate republican' is the wordplay.
'want' becomes 'dearth' (both can mean a lack or scarcity).
'to eliminate' indicates named letters should be taken away.
'republican' becomes 'R' (abbreviation).
'dearth' with 'r' taken away is 'DEATH'.
(Other definitions for death that I've seen before include "Fatality" , "End of life" , "Final moments" , "Hated (anag) - curtains (informal)" , "Hated (anag) -- expiry" .)