Spin at extremely giddy speed (6)
I believe the answer is:
gyrate
'spin' is the definition.
('gyrate' can be a synonym of 'spin')
'at extremely giddy speed' is the wordplay.
'at' is a charade indicator (letters next to each other).
'extremely' suggests removing the centre.
'speed' becomes 'rate' (rate is a kind of speed**).
'giddy' with its centre removed is 'gy'.
'gy' put next to 'rate' is 'GYRATE'.
(Other definitions for gyrate that I've seen before include "Move with a circular motion" , "Spiral about a point" , "Revolve, whirl" , "Turn" , "Move spirally" .)