With last of deliveries, spinner gets close (4)
I believe the answer is:
stop
'close' is the definition.
(thesaurus)
'with last of deliveries spinner' is the wordplay.
'with' means one lot of letters go next to another.
'last of' suggests the final letters.
'spinner' becomes 'top' (something that spins).
The last letter of 'deliveries' is 's'.
's' put next to 'top' is 'STOP'.
'gets' acts as a link.
(Other definitions for stop that I've seen before include "colon, say" , "port of call" , "Plug; cease" , "Go no further" , "End - period" .)