Consumer gets special rate after last time (5)
I believe the answer is:
eater
'consumer' is the definition.
(consume can mean to eat)
'special rate after last time' is the wordplay.
'special' is an anagram indicator.
'after' means one lot of letters go next to another.
'last' suggests the final letters.
The last letter of 'time' is 'e'.
'rate' is an anagram of 'ater'.
'ater' after 'e' is 'EATER'.
'gets' acts as a link.
(Other definitions for eater that I've seen before include "Consumer at table" , "diner" , "One consuming" , "Type of apple" , "Taker of food" .)