Discard last of food? That's annoying situation (4)
I believe the answer is:
bind
'that's annoying situation' is the definition.
(as in being in a bind)
'discard last of food?' is the wordplay.
'discard' becomes 'bin' (I've seen this before).
'last of' indicates one should take the final letters.
The final letter of 'food' is 'd'.
'bin'+'d'='BIND'
(Other definitions for bind that I've seen before include "Tie, fasten" , "This weed" , "Senior figure" , "Restrict" , "Impose a contractual obligation on (someone)" .)