I didnt sign anything with TT. I've got a month to month with Afrihost. Tbh I dont find it that bad. Definitely not bad enough to go through the schlep of cancelling and applying for something new. Just every now and then I get some buffering/latency issues and hence the original q, was wondering if priority would help.
No, it won't. I was on Afrihost Business Uncapped in 2014-15 when it was still fully unshaped/uncapped. 3 months worth of to and fro resulted in no resolution as to why I had constant buffering on my account all of a sudden for no good reason, yet a test account which was supposedly configured identically, didn't hickup once over an entire weekend. Moved back to my account, which they even "recreated from scratch", same issues back immediately. Downloads were at 100% speed, even torrents with enough seeds.
Moved to CrystalWeb which had no streaming issues until the infamous DDoS meltdown of April 2018, when I moved to Vox which was fine as well until August when I moved to fibre.
In short, if you're in the mood for a protracted runaround with Afrihost whenever you have an issue, sure, otherwise finde a real ISP. I would recommend Vox.