Petition about it after oil's spilt (7)
I believe the answer is:
solicit
'petition' is the definition.
(thesaurus)
'about it after oil's spilt' is the wordplay.
'about' becomes 'c' (abbreviation for 'circa'**).
'after' means one lot of letters go next to another.
'spilt' indicates an anagram.
'oils' anagrammed gives 'soli'.
'c'+'it'='cit'
'cit' put after 'soli' is 'SOLICIT'.
(Other definitions for solicit that I've seen before include "Try to obtain (something) from someone" , "Proposition" , "Make request (for business etc)" , "Request, induce" , "Ask earnestly,seek to obtain" .)