Possible Clues:

• Move right outside capital to find pet
• Little bird, one moving around Latvian capital
• One moving perhaps around Baltic capital sees parakeet
• Bird to move over river descending on one fish
• Begin to move Latvian capital at the middle of March for one flying from Australia
• Move fake by artist, in hindsight. 'Whistler' that's perching in the room?
• Aussie bird, one moving around Baltic capital
• Remove kit with a redhead bird
• Small parrakeet
• Aussie native wanting to shoot drugs, stashing equipment