Police officers fill their bellies and throw up (8)
I believe the answer is:
disgorge
'throw up' is the definition.
(synonyms)
'police officers fill' is the wordplay.
'police' becomes 'dis' (detective inspectors or DIs).
'officers fill' becomes 'gorge' (I can't justify this - if you can you should believe this answer much more).
'dis'+'gorge'='DISGORGE'
'their bellies and' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for disgorge that I've seen before include "Throw up, regurgitate" , "So rid egg? (anag)" , "yield under pressure" .)