Feeling fed up dropping off envelopes, went and quit (5)
I believe the answer is:
ennui
'feeling' is the definition.
(ennui is a kind of feeling)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for ennui that I've seen before include "What's tedious and instils such listlessness" , "Low interest rate" , "Feeling when tired of life?" , "Mental weariness" , "Sense of tedium" .)