Drones coming from bagpipes enrage eloquent spokesperson at the opening (4)
I believe the answer is:
bees
'drones' is the definition.
(I've seen this in another clue)
'bagpipes enrage eloquent spokesperson at the opening' is the wordplay.
'at the opening' indicates taking the first letters.
The first letters of 'bagpipes enrage eloquent spokesperson' is 'BEES'.
'coming from' acts as a link.
(Other definitions for bees that I've seen before include "Four-winged insects" , "Busy insects" , "Drones and workers" , "Apiary inhabitants" , "They are kept in an apiary" .)