Recording label to fasten inside (6)
I believe the answer is:
taping
'recording' is the definition.
(I know that taping is a type of recording)
'label to fasten inside' is the wordplay.
'label' becomes 'tag' (synonyms).
'to fasten' becomes 'pin' (pinning is a kind of fastening).
'inside' indicates putting letters inside.
'tag' going around 'pin' is 'TAPING'.
(Other definitions for taping that I've seen before include "Recording" , "Fastening" , "Securing" , "Wrapping" .)