Delivery company starts to examine this complaint (5)
I believe the answer is:
upset
'complaint' is the definition.
(I've seen this before)
'delivery company starts to examine this' is the wordplay.
'delivery company' becomes 'ups' (I've seen this in other clues).
'starts to' suggests taking the first letters.
The initial letters of 'examine this' is 'et'.
'ups'+'et'='UPSET'
(Other definitions for upset that I've seen before include "Discountenanced" , "Caused grief" , "Spilt - annoyed" , "Aggrieved" , "emotional" .)