History of disc — part of it first (5,6)
I believe the answer is:
track record
'history' is the definition.
(I've seen this before)
'disc part of it first' is the wordplay.
I cannot really understand how this works, but
'disc' could be 'record' (synonyms) and 'record' is found within the answer.
'part' could be 'track' (I have seen 'Part of record' mean 'track' so perhaps 'part' could also mean 'track') and 'track' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'of' is the link.
(Other definitions for track record that I've seen before include "Previous achievements" , "Sum of recognised accomplishments" , "(A person's) past achievements" , "Information on past performance" , "Past account" .)