I should mention that I wouldn't run this past my manager as I'm sure he would say no. He likes to maintain the status quo and I don't think he would like me rocking the boat. The partner is not in my management chain, so I'm not really going over his head.
Yes, you are. A partner is a very high-ranking member of a business, possibly even a co-owner, depending on how the business was set up. Assuming this person really is a partner in that sense, they outrank most or all of your reporting chain, so this is roughly equivalent to reaching out directly to a C-suite executive. You should not do that. Regardless of whether this person is technically in your reporting chain or not, you would absolutely be going over your boss's head, and your boss would rightly perceive this as insubordination.
But let's assume that by "partner" you actually meant something more like "executive" - a high-ranking middle manager, or something like that. It's still a bad idea. Why? Let's go through the likely outcomes:
- Your email is ignored. You accomplish nothing.
- The executive likes your idea, and wants you to work on it. So they contact your boss asking if you are available.
- The executive likes your idea, and tells your boss about how smart it was.
- The executive dislikes your idea, and complains to your boss that you are wasting their time.
- The executive takes your idea and runs with it, without involving you. Then it probably won't show up on your performance evaluation and you will probably get nothing out of it.
In any situation where your boss first learns of this from the executive, they are going to be upset that you went behind their back. It is going to damage your working relationship, and possibly put your career at risk. On the other hand, you seem to gain very little from it in any of these outcomes. Even if the executive is pleased, they have little control over your career, especially compared to your boss. So I simply cannot recommend doing this.