Spread support next to an entrance (9)
I believe the answer is:
propagate
'spread' is the definition.
(I know that propagate is a more specific form of spread)
'support next to an entrance' is the wordplay.
'support' becomes 'prop' (prop up can mean to support).
'next to' is a charade indicator (letters next to each other).
'an' becomes 'a'.
'entrance' becomes 'gate' (type of entrance).
'prop'+'a'+'gate'='PROPAGATE'
(Other definitions for propagate that I've seen before include "Publicise" , "Breed from parent stock" , "Develop" , "broadcast" , "Grow (plants) or spread (ideas)" .)