What qualifications does Chekov have to be chief of security - he was naive, scientifically trained, and he got beat up pretty much every time he ever got into a fight.
And he also had a two-and-a-half year gap that we simply don't know what he was doing. So for all we know, he decided he wanted to be in Security and switched tracks. Much like Sulu being a blue-shirt in Where No Man...
then moving to the helm in the series proper.