im not sure about a 7 letter word, but i do know i 8 letter word that starts with s and means the right to vote, the word is... sufferage.
slickers
Dictator
friction
assassin
An 8 letter word that means the inside of anything might be "interior." This word has 8 letters and would probably fit your crossword puzzle clue.
"Endorsement" is an 8-letter word that means official approval or support.
Isolated
allocate
birthday
accurate
transfer
famished
friction
Egoistic
The 8-letter "f" word in science that means force is "friction."
memorize