Smaller left half starts to shimmy and shake (4)
I believe the answer is:
less
'smaller' is the definition.
(less great in size)
'left half starts to shimmy and shake' is the wordplay.
'half' indicates taking half.
'starts to' indicates taking the first letters.
'and' means one lot of letters go next to another.
'shake' becomes 's' (this might be a standard abbreviation which I don't know about).
The initial letter of 'shimmy' is 's'.
'left' cut in half is 'le'.
'le'+'s'+'s'='LESS'
Can you help me to learn more?
(Other definitions for less that I've seen before include "In smaller quantity" , "Fewer; minus" , "Minus; not so much" , "more, as they say" , "Comparative of 'a little'" .)