Capital initially invested in urchin’s discharge (10)
I believe the answer is:
bratislava
'capital' is the definition.
(capital of Slovakia)
'initially invested in urchin's discharge' is the wordplay.
'initially' suggests taking the first letters.
'in' indicates putting letters inside.
'urchin's' becomes 'brat's' (both can mean a child).
'discharge' becomes 'lava' (lava is discharged from a volcano).
The first letter of 'invested' is 'i'.
'i' put inside 'brats' is 'bratis'.
'bratis'+'lava'='BRATISLAVA'
(Other definitions for bratislava that I've seen before include "Capital of Slovakia" , "Capital of the Slovak Republic" , "Slovakian capital" , "City" .)