Kate was last seen wearing the jacket in a short film, where she is seen roaming in the countryside alongside radio presenter Roman Kemp.
The clip was filmed in support of the Shaping Us campaign at an undisclosed location in Hertfordshire last month.
The Princess launched her Shaping Us initiative last week – an ambitious campaign described as her “life’s work” and aimed at raising the profile of the early years’ development of children.
Kate and Roman discussed the importance of mental well-being and relationships, and how by nurturing children in the earliest years of their life, society can help build a community of healthy, happy adults.