The star shown here is the Efficiency badge awarded originally to Volunteers, later to Territorials. In the Territorial force this was awarded for being judged efficient four time. It continued to be used in the TA as Badges, Arm, Stars, Worsted, SD, Efficiency, TA.
Grumpy's book illustrates it as 33 and notes that it was not declared obsolete until 1952.
Jon
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