Don't have stabilisers, which does surprise you (4)
I believe the answer is:
rock
'surprise you' is the definition.
'rock' can be an answer for 'surprise' (thesaurus). I am not certain of the 'you' bit.
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for rock that I've seen before include "Music; diamond" , "Hard confectionery made in sticks" , "musical genre?" , "Modern music with a heavy beat" , "Edinburgh - -" .)