Possible Clues:

• Precious stone from a Queen, you said -- a queen in Eastern state
• Cool shade
• By virtue of being fighting man, following a colour
• Pale bluish-green
• Beryl's answer as member of the army at sea
• [Gemstone]
• This gemstone is a greenish-blue form of beryl
• Gemstone a queen pinned to a soldier
• Shade named for a mineral
• Its deep blue variety is called maxixe