Royalty surrounded by bigwigs - the snakes! (6)
I believe the answer is:
vipers
'the snakes' is the definition.
(viper is a kind of snake)
'royalty surrounded by bigwigs' is the wordplay.
'royalty' becomes 'er' (abbreviation for Elizabeth Regina).
'surrounded by' means one lot of letters goes inside another.
'bigwigs' becomes 'vips' (I've seen this before).
'er' going inside 'vips' is 'VIPERS'.
(Other definitions for vipers that I've seen before include "Snakes, perhaps in bosoms" , "Venomous snakes" , "21 [SNAKES]" .)