Horrified to have a good speed limited (6)
I believe the answer is:
aghast
'horrified' is the definition.
(I know that horrified can be written as aghast)
'have a good speed limited' is the wordplay.
'have a good' becomes 'ag' (I can't explain this - if you can you should give a lot more credence to this answer).
'speed' becomes 'haste' (haste is a kind of speed).
'limited' means to remove the last letter.
'haste' with its last letter taken off is 'hast'.
'ag'+'hast'='AGHAST'
'to' is the link.
(Other definitions for aghast that I've seen before include "Shocked, dumbfounded" , "Filled with terror" , "Amazed" , "Stupefied with horror" , "What's carried in bag has teacher" .)