It's all down to what is agreed between Carter and Chester.
There is no rule to say he can't get another job.
There is no rule to say he has to be paid monthly.
It's an agreement between them.
If you leave a company by mutual consent you have a termination agreement to state the rules. This is no different. They may have written it down or may not.
I'd also say, coaches wages don't come under the salary cap rules so the payment does not affect that.
And because of that. The payment can come from anywhere, not necessarily out of club funds.