Kelvin on tabloid's doomed (4)
I believe the answer is:
sunk
'doomed' is the definition.
(I've seen this before)
'kelvin on tabloid's' is the wordplay.
'kelvin' becomes 'k' ('K' can be a synonym of 'kelvin').
'on' is a charade indicator (letters next to each other).
'tabloid' becomes 'sun' (The Sun, UK newspaper).
'k' after 'sun' is 'SUNK'.
(Other definitions for sunk that I've seen before include "suffered decline" , "(Has) disappeared beneath the waves" , "Submerged" , "Gone under" , "Sent to bed" .)