Simple enough question :~} It depends on how you want to proceed. You can either find a partner and start working toward competing in amateur competitions or you can find a competent pro and do pro am.
Actually either way the most important thing is to find a competent instructor because you'll need one to improve your skills. To find one you like go to a couple of comps and watch the pros until you find one who looks like a good fit. Then go sit in and listen into one or two of his/her lessons to see if they teach in a way that is compatible with how you learn. If you can find a partner it's great but it isn't mandatory and some people don't want one at all. It is up to you...follow your bliss.
As Belle said, you don't need a partner if you go Pro-Am. However, this is an expensive option. If you want to compete as an amateur, I don't see how you can do that without a partner. You need to train together and have good working relationship. There has to be some chemistry if you are dancing latin. So, yes, find a partner, then find a pro who teaches competitive couples.
If you are just starting you should just take lessons in technique first and don't think too much about a partner yet.If you have or look like you are trying to craft your dance correctly you will attract the right kind of dance parter.