To unlock a Clan Capital appearance, you and your clanmates must participate in the "Union of Triumph" tournament to earn Union Tokens. The Capital appearance will unlock automatically once your Clan has accumulated 900K Union Tokens.
You can change the appearance of the Clan Capital and examine the bonus that the appearance grants in the Union of Triumph interface: click the appearance image in the Union interface or click the "Capital appearance" button in the Clan Capital information window.