Former copper, extremely sincere, giving pardon (6)
I believe the answer is:
Here is my best explanation:
'pardon' is the definition.
('excuse' can be a synonym of 'pardon')
'former copper extremely sincere' is the subsidiary indication.
'former' becomes 'ex'.
'copper' becomes 'cu' ('Cu' can be a synonym of 'copper').
'extremely' suggests removing the centre.
'sincere' with its centre removed is 'se'.
'giving' is the link.
(Other definitions for excuse that I've seen before include "Apology", "Allow to be released from a duty", "Defence, justification", "Pardon or justify", "Seek to justify (a fault)", "Absolve", "Defence of offensive behavior", "Make apologies for", "Forgive or overlook an offence" and "Pardon, or release from obligation".)