Very legitimate petition (7)
I believe the answer is:
solicit
'petition' is the definition.
(both can mean to request or implore)
'very legitimate' is the wordplay.
'very' becomes 'so' (both can mean 'extremely').
'legitimate' becomes 'licit' (synonyms).
'so'+'licit'='SOLICIT'
(Other definitions for solicit that I've seen before include "Ask earnestly,seek to obtain" , "Ask (favour)" , "Accost - request" , "Tout" , "Make request (for business etc)" .)