Crossword Genius

Deliveries proceed quickly in storm (7)

Ross

I believe the answer is:

overrun

'storm' is the definition.
(thesaurus)

'deliveries proceed quickly' is the wordplay.
'deliveries' becomes 'over' (I've seen this before).
'proceed quickly' becomes 'run' (I've seen this before).
'over'+'run'='OVERRUN'

'in' is the link.

(Other definitions for overrun that I've seen before include "Cover - attack" , "Go on too long (of a performance)" , "Exceed (eg, time, cost)" , "Plagued by" , "Heavily defeat" .)

I've seen this clue in The Everyman puzzle in The Observer.
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