The remainder live around the capital of Uganda (7)
I believe the answer is:
residue
'the remainder' is the definition.
('residue' can be a synonym of 'remainder')
'live around the capital of uganda' is the wordplay.
'live' becomes 'reside' (residing is a kind of living).
'around' means one lot of letters goes inside another.
'the capital of' says to take the initial letters.
The first letter of 'uganda' is 'u'.
'reside' going around 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "Matter left behind after other parts have been taken away" , "What's left" , "Small amount remaining" , "Leftovers" , "Lees, dregs" .)