thanks for posting. Whilst the Edinburgh Fringe Festival is hugely successful, event organisers have to compete hard to fill their venues as there is so much going on. I don’t know whether you have seen this already but I’ve just found this handy [guide to promoting your show]
(https://www.edfringe.com/uploads/docs/participants/Fringe%20Guide%20to%20Promoting%20your%20Show.pdf) at the Fringe. It seems quite comprehensive.
I’ve not worked on the Fringe myself but as a general rule, I’ve found organisers are hungry for event content to talk about early on so the sooner you get your press release to the Fringe media office the better. If they’re willing to place competitions with appropriate media work with them by offering a pair of tickets as a prize, a backstage tour, a meet and greet, signed merchandise or whatever you can as potential prizes. I’d also recommend getting there the week before if you can and getting posters put up wherever you can - community noticeboards, pubs, clubs, gyms, bed & breakfasts, hotels, etc.
Hope that’s helpful! Best of luck!