Support, encourage (7)
I believe the answer is:
promote
This clue is a double definition.
'support' is the first definition.
(promoting is a kind of supporting)
'encourage' is the second definition.
(synonyms)
(Other definitions for promote that I've seen before include "Raise to higher grade" , "Advocate, advance" , "Actively support" , "Raise to higher rank" , "Contribute to progress or growth" .)