No

While removing Patrick from his job may be an option if you have a policy against moonlighting or tardiness, you need to meet with Patrick and discuss the situation. It is preferable to find a solution other than asking him to give up his other job, if possible. If no other accommodation can be made (i.e., changing Patrick's work hours or having Patrick work another shift at the restaurant) you might want to suggest that Patrick give up the job in order to protect his job with you.