If that is the case the hat badge that preceded the Kepi one in the photo is this one which was worn by the 4th RV on the shako:
https://www.the-saleroom.com/en-gb/a...c-a5ee009b2a7b
This preceded that hat in your photo and it was then replaced by the glengarry in the earlier link.
The glengarry was replaced by the Field Service Cap (side cap) which was often worn badgeless or with a collar on it. This in turn was replaced by the Norfolk Britannia in a Wreath cap badge with the VB title on the Brodrick and then peaked cap.