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 "Seek to justify (a fault)", "Mitigate; forgive", "Apology", "Allow to be released from a duty", "Plea; let off", "Pardon or forgive", "Pardon, or release from obligation", "Defence of offensive behaviour", "Absolve" and "Upstanding community members".)