Sly, unsteady boozer, who's quite slim (5)
I believe the answer is:
sylph
'quite slim' is the definition.
I can't judge whether this defines the answer.
'sly unsteady boozer' is the wordplay.
'unsteady' is an anagram indicator.
'boozer' becomes 'ph' (I can't explain this - if you can you should give a lot more credence to this answer).
'sly' with letters rearranged gives 'syl'.
'syl'+'ph'='SYLPH'
'who's' acts as a link.
Can you help me to learn more?
(Other definitions for sylph that I've seen before include "Slender, graceful female" , "Slim female" , "Imaginary (female) being" , "Thin and graceful female" , "Girl with slender figure" .)