This badge design was worn from circa 1907 into the 1950s. Before that the Brodrick cap was worn with the round Victorian version.
https://greenhowards.org.uk/brodrick-cap/
It's design remained unchanged until it was replaced by the shorter 1950s version.
There was a plastic economy version circa 1944 and a WW2 era version which was made with a crown rather than the coronet.
So you have a start and an end date and periods when plastic or crown versions were also worn but there is no way to tell just how old it is or from which war.
Alan