I figure this is as fine a place to ask as anywhere else... what is the extra badge that Pelia wears? I don't recognize it and I haven't spotted any close ups on it to get a good look
I don't think it's been identified. However, she is a long-serving Starfleet officer, and was both a Chief Fleet Inspector and a (probably senior) instructor at Starfleet Academy before joining the Enterprise, so you could make a reasonable guess that it's a badge of seniority/advanced qualification.