Sorry about the slight blur to this shot (darn it, I knew I should have taken another one!) -- this is a despatch case used by Governor Sir George Grey. In the late 1840s, he came in as Governor and listened to the tide of land hunger amongst the settlers then, overturning Fitzroy's "dealing only with the Crown" reforms; in the 1860s, he stepped right into the ferment between Maori and settlers, and let loose the dogs of war; and in the 1870s he tried, unsuccessfully, to defend the constitution he himself had inaugurated, but could only stand back and watch as the provinces dissolved. He also tried setting up a MAF officer's nightmare of a Kawau Island stuffed-full of exotic beasties (especially wallabies). He did leave a valuable book and manuscript collection which helped to kick start the Auckland City Library in the 1880s, and he was a friend to Sydney Margaret Hamilton. Image below from Alexander Turnbull Library, via Wikipedia.
This, according to the museum's display listing, is said to be a bugle sounded during the Battle of Rangiriri, 1863. Details on this battle during the Waikato War at the link, via NZETC.