Starts inserting files in elegant pigeonhole (8)
I believe the answer is:
'pigeonhole' is the definition.
'starts inserting files in elegant' is the wordplay.
'starts' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'elegant' becomes 'classy' (I've seen this before**).
The initial letters of 'inserting files' is 'if'.
'if' inserted within 'classy' is 'CLASSIFY'.
(Other definitions for classify that I've seen before include "Arrange by category" , "Categorise or pigeonhole" , "Make secret for security reasons" , "catalogue?" , "Arrange in divisions" .)