Give up extremely detestable sort of meat (7)
I believe the answer is:
Here is my best explanation:
'give up' is the definition.
('deliver' can be a synonym of 'give up')
'extremely detestable sort of meat' is the subsidiary indication.
'extremely' means to remove the middle letters.
'sort of meat' becomes 'liver' (**).
'detestable' with its centre removed is 'de'.
(Other definitions for deliver that I've seen before include "Make a speech - free", "Bring letter or rescue", "Bring (letters, etc)", "Handover", "Hand over (letter)", "Hand over (to someone)", "Transport", "Render", "Bring into the world - set free" and "Supply, hand over".)