Right to support very good petition (7)
I believe the answer is:
solicit
'petition' is the definition.
(both can mean to request or implore)
'right to support very good' is the wordplay.
'right' becomes 'licit' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'to support' means one lot of letters go next to another (in a down clue, some letters hold others up).
'very good' becomes 'so' (as in the adjectival form 'just so!').
'licit' after 'so' is 'SOLICIT'.
Can you help me to learn more?
(Other definitions for solicit that I've seen before include "Request urgently and/or persistently" , "Try to obtain (something) from someone" , "Seek to obtain, ask earnestly" , "Invite, beg for" , "Ask (favour)" .)