Kent, just like Cordelia, is only rewarded with punishment for his honestly, loyalty and truthfulness. He, when he sees how Lear responds to Cordelia after she refuses to exaggerate and lie about her love for him as her sisters have done, tries to remonstrate with Lear and make him take back his hasty words. When he goes on to insist in very vocal terms that Lear has made a mistake, Lear sees this as a challenge to his authority that is akin to treason, and punishes Kent with banishment. Note what he says to Kent in Act I scene 1:
Our potency made good, take thy reward:
Five days we do allot thee for provision
To shield thee from diseases of the world.
And on the sixth to turn thy hated back
Upon our kingdom. If on the next day following
Thy banished trunk be found in our dominions,
The moment is thy death.
Lear therefore gives Kent five days to leave the country, saying that if he is found in England after the sixth day, he will be punished by death. The parallel between Kent and Cordelia is clear: both are punished for telling the truth. The audience's impression of Lear as a man who is unable to accept the truth is confirmed.