Illegal activity carried out next to Rio (9)
I believe the answer is:
extortion
'illegal activity carried' is the definition.
I can't judge whether this definition defines the answer.
'out next to rio' is the wordplay.
'out' indicates an anagram.
'next'+'to'+'rio'='nexttorio'
'nexttorio' is an anagram of 'EXTORTION'.
Can you help me to learn more?
(Other definitions for extortion that I've seen before include "Extraction of money with menaces" , "The obtaining of money by force or threat" , "Blackmail" .)