Finished making deliveries (4)
I believe the answer is:
over
I believe this clue is a double definition.
'finished' is the first definition.
(similar in meaning)
'deliveries' is the second definition.
(I've seen this before)
'making' is the link.
(Other definitions for over that I've seen before include "Completely ended" , "Finished; six balls" , "Passed" , "Finished like cricket period" , "Action far more drastic than necessary" .)