Vice-Regal (or more usually viceregal) is the adjective formed from viceroy. -
(WordReference Dictionary)viceroy /ˈvʌɪsrɔɪ/
a ruler exercising authority in a colony on behalf of a sovereign.
The party means the group of people including the viceroy.
So it's a more formal version of 'the viceroy and his retinue'.
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