Look back! Old Chinese chairman about to get a shark! (4)
I believe the answer is:
mako
'shark' is the definition.
(mako is a kind of shark)
'look back old' is the wordplay.
'look back' becomes 'mak' (I can't justify this - if you can you should give a lot more credence to this answer).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'mak'+'o'='MAKO'
'chinese chairman about to get a' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for mako that I've seen before include "NZ tree" , "Shark" .)