Possible Clues:

• Sleeveless garment worn under a jacket
• Sounds like instruction to jettison Ulster as part of suit
• Garment was falling short, one to cast out
• Garment
• Hesitate to be seen around Ascot clumsily wearing this
• A “vest” in the US
• Item of clothing from week at Ascot, I fancy
• Garment under a doublet