The most common and most likely answer to this crossword clue is the 10 letter word WELLINGTON
I've seen this crossword clue in Financial Times
W
E
L
L
I
N
G
T
O
N
More clues leading to the result WELLINGTON
- Western jazz musician gets the boot
- Foot could be protected by this prime minister
- Something afoot in the capital
- Capital city: possible location of this setter, reportedly?
- Spring fashion involves wearing a bit of Gucci footwear
- Healthy and popular, with good weight? Capital
- Dish of beef wound round fish covering
- Duke with capital
- Rising to the surface and new: stifling to boot
- Navy-bottomed bathrobe material that’s reduced to boot
Buddy explains!

The straight part
We know that "Capital city" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case capital city = wellington.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WELLINGTON mean?
WELLINGTON noun- A Wellington boot.
- Meat baked in a puff pastry.