Justice threw in sponge in Ely, losing heart (6)
I believe the answer is:
equity
'justice' is the definition.
(I know that equity is a type of justice)
'sponge in ely losing heart' is the wordplay.
'sponge' becomes 'quit' (I am not sure about this - if you are sure you should believe this answer much more).
'in' is an insertion indicator.
'losing heart' suggests removing the centre.
'ely' with its centre taken out is 'ey'.
'quit' going within 'ey' is 'EQUITY'.
'threw in' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for equity that I've seen before include "Fairness; shareholding" , "Value of a property less debt" , "Fairness for actors' trade union" , "The ownership interest of shareholders in a company" , "Fair play - actors' union" .)