Stick and stone grow (9)
I believe the answer is:
propagate
'grow' is the definition.
(thesaurus)
'stick and stone' is the wordplay.
'stick' becomes 'prop'.
'and' means one lot of letters go next to another.
'stone' becomes 'agate' (agate is a type of stone).
'prop'+'agate'='PROPAGATE'
(Other definitions for propagate that I've seen before include "broadcast" , "widely spread" , "Increase by natural process" , "Produce more" , "Disseminate" .)