Greatly object to the coin that’s no longer currency (8)
I believe the answer is:
farthing
'currency' is the definition.
(farthing is a kind of currency)
'greatly object' is the wordplay.
'greatly' becomes 'far' (I can't justify this - if you can you should give a lot more credence to this answer).
'object' becomes 'thing' (an object is a thing or item).
'far'+'thing'='FARTHING'
'to the coin that's no longer' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for farthing that I've seen before include "One quarter of an old penny: measure of land in old England" , "Smallest coin once" , "Old piece" , "once of minimal value" , "of negligible value" .)