Criminal record briefly enthralled female, extremely elegant (3,5)
I believe the answer is:
rap sheet
'criminal record' is the definition.
(a rap sheet is a police record)
'briefly enthralled female extremely elegant' is the wordplay.
'briefly' means to remove the last letter.
'enthralled' becomes 'rapt' (I've seen this before).
'female' becomes 'she' ('she' refers to a woman).
'extremely elegant' becomes 'et' (I can't justify this - if you can you should give a lot more credence to this answer).
'rapt' with its last letter taken away is 'rap'.
'rap'+'she'+'et'='RAP SHEET'
Can you help me to learn more?
(Other definitions for rap sheet that I've seen before include "record of arrests" , "Where to find previous" , "Criminal record, colloquially" , "'Written record of charges (3,5)'" .)