While such a collaboration might, indeed, be a conflict of interest, that doesn't necessarily make it impossible to manage. But it takes some planning so that the conflict doesn't result in any improper action.
That assumes that you, the head, and maybe the entire department have a way, policies, to manage the potential conflict in a way that is fair to all. The dean (or provost,..., depending) might need to have a say.
In particular, the head might need to step out of certain decisions that affect you either positively or negatively and defer to others, perhaps a dean, or perhaps a committee.
I've been in situations where I wouldn't consider collaboration with a superior when I couldn't trust the system as a whole. I've also been in situations where such collaboration would be entirely comfortable.
The problem isn't the CoI itself, but how the conflict (potential conflict, actually) can be handled. A CoI isn't an automatic ban on collaboration, or cooperation generally. Just don't make assumptions that all is well or that all is bad.