In a democrativc system, every citizin who is a member of a political party can try to run for the Knesset on that party's list. Noam shalit probably has enough experience and certainly enough integrity. He just might find that integrity doesnot bring you very far in Israeli politics.
About 2,000 demonstrators protest 'occupation policy and fascist settlers' in Nazareth (Haaretz)
from the article: Neither Lapid nor Shalit deserves to be in politics