Run quickly to cover case of affair in capital (6)
I believe the answer is:
harare
'capital' is the definition.
(capital of Zimbabwe)
'run quickly to cover case of affair' is the wordplay.
'run quickly' becomes 'hare' (hare can mean to run fast).
'to cover' indicates putting letters inside.
'case of' suggests removing the centre (outsides of).
'affair' with its middle removed is 'ar'.
'hare' placed around 'ar' is 'HARARE'.
'in' is the link.
(Other definitions for harare that I've seen before include "Capital of Zimbabwe" , "Zimbabwe's capital" , "African capital" , "capital abroad" , "City in Zimbabwe" .)