I applied in 2015 for a tier 4 visa to study in the UK. I got refused due to insufficient funds (The real reason is that I didn't leave the money in the bank for 28 days). So I applied again last year (2016) without fast track and was granted a visa. I went to an international college so the visa only lasted for a year. Now this year, I want to apply again for another tier for a visa which lasts for the whole 3 years of my course. I want to find out if it is possible to fast track seeing as I was granted a visa just last year.
You don't say where you're applying from but nothing should stop you using the priority service. This won't change or influence the outcome of your visa at all, it only means that your application is placed at the front of the queue once it arrives for consideration. There is no guarantee it will be processed in a shorter time frame, especially if there are extenuating circumstances to consider.
Using the priority visa service does not imply or guarantee in any way that your visa application will be successful. All visa applicants must meet the requirements of the UK Immigration Rules. The amount paid for the priority service, as well as the visa application fee, is not refundable if the visa application is refused or, in exceptional cases, takes longer to process.