Capital that's eastern in spirit (5)
I believe the answer is:
seoul
'capital' is the definition.
(capital of South Korea)
'eastern in spirit' is the wordplay.
'eastern' becomes 'e'.
'in' means one lot of letters goes inside another.
'spirit' becomes 'soul' (soul is a kind of spirit).
'e' going within 'soul' is 'SEOUL'.
'that's' acts as a link.
(Other definitions for seoul that I've seen before include "Asian capital" , "Olympic venue" , "South Korea capital" , "South Korean capital" , "19 [EASTERN] capital" .)