Extremely giddy speed to revolve! (6)
I believe the answer is:
gyrate
'to revolve' is the definition.
(I know that gyrate is a more specific form of go around)
'extremely giddy speed' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'speed' becomes 'rate' (the speed at which something happens).
'giddy' with its middle taken out is 'gy'.
'gy'+'rate'='GYRATE'
(Other definitions for gyrate that I've seen before include "Twirl" , "wheel" , "Revolve, whirl" , "Wind in a spiral" , "Move in a circle or spiral" .)