Last of the latecomers gets rotten seat (6)
I believe the answer is:
saddle
'seat' is the definition.
(saddle is a kind of seat)
'last of the latecomers gets rotten' is the wordplay.
'last of' suggests the final letters.
'gets' is a charade indicator (letters next to each other).
'rotten' becomes 'addle' (I've seen this before).
The final letter of 'latecomers' is 's'.
's'+'addle'='SADDLE'
(Other definitions for saddle that I've seen before include "Jockey's seat" , "piece of lamb?" , "A horseman's seat" , "load" , "Chafed by riding" .)