Spread through (7)
(Other definitions for overrun that I've seen before include "area beyond end of airstrip" , "Inundate, infest" , "Exceed (estimated cost)" , "Exceed (allowed cost/time)" , "Exceed (allowed time/cost)" .)
(Other definitions for suffuse that I've seen before include "Flood through" , "Of colour, spread slowly throughout" , "Spread; permeate" .)
'spread through' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for pervade that I've seen before include "Diffuse through the whole" , "Permeate" , "Spread throughout" , "Spread right through" , "Deprave (anag)" .)