Trainee misplaced the last of finder's fee (8)
I believe the answer is:
retainer
'fee' is the definition.
(retainer is a kind of fee)
'trainee misplaced the last of finder's' is the wordplay.
'misplaced' indicates anagramming the letters (letters in the wrong places).
'the last of' says to take the final letters.
The final letter of 'finder' is 'r'.
'trainee' anagrammed gives 'retaine'.
'retaine'+'r'='RETAINER'
(Other definitions for retainer that I've seen before include "given payment in advance" , "Fee paid to book the services of someone" , "Down-payment for Eritrean" , "Fee; long-term servant" , "Family servant of long standing - fee charged in advance" .)