A subject can 'hang' of course, depending on what went before. If, as Lisa now explains, she is writing a 'bullet-point' after an initial explanation then everything changes completely and the subject is pre-stated and implicit.
It needs to be just one line to explain that as a team leader/supervisor I can communicate well with team members and bring everyone together as a team....
I am a natural leader with excellent communication skills, which I put to good use building successful and collaborative teams. (edit to what you actually do)
It is not enough to say what you are good at, you need to demonstrate how/why your skills are useful/applicable to the job at hand (HR would use the word "demonstrable").
conversable is not a word, it could be the adjective to converse but that is not listed in the OED. Anyway maybe...."An approachable and receptive team leader/Supervisor who can unite a team"