Tape class outside of class (8)
I believe the answer is:
cassette
'tape' is the definition.
(cassette tape is a kind of tape)
'class outside of class' is the wordplay.
'class' becomes 'caste' (type of social class).
'outside of' indicates putting letters inside.
'class' becomes 'set' (I've seen this before).
'caste' enclosing 'set' is 'CASSETTE'.
(Other definitions for cassette that I've seen before include "Music tape" , "Vintage recording" , "Test case about tape container" , "Recorder would accommodate this" , "Spool of tape" .)