Capital's name finally included in new airport (8)
I believe the answer is:
pretoria
'capital's' is the definition.
(administrative capital of South Africa)
'name finally included in new airport' is the wordplay.
'finally' says to take the final letters.
'included in' means one lot of letters goes inside another.
'new' indicates anagramming the letters.
The last letter of 'name' is 'e'.
'airport' is an anagram of 'prtoria'.
'e' going into 'prtoria' is 'PRETORIA'.
(Other definitions for pretoria that I've seen before include "Administrative capital of South Africa" , "Executive capital of South Africa" , "Pirate or a South African city, strangely" , "Administrative capital of South African" , "Capital city" .)