Imagine how relaxed you'll feel afterwards... This pretty much always helped me, and I was relaxed after the test... (and usually wrote well...)
Also, try to study enough, go through everything and tell yourself your sub-conscious can remember most things.. In hypnosis, people recalled stuff they only briefly read one time... The trick is to remember it all upon recall.. (so repetition is good) Also choose to trust your sub-conscious to remember it..
Write out notes and mind maps, use color.. There are lots of study tips in books and in articles and online..
Also make sure you have eaten (ideally something with anti-stress vitamins/minerals, like magnesium, avoid sugar/caffeine) Some walking/exercise before studying can help to focus too..
If the clock is too loud, earplugs? (Though you may be bothered by noise after putting them out, so hm?)
You can also look away from people/clocks etc. Also know if people finished fast, they may have finished wrong too.. so it's better to take time and double-check.. I often finished last or among the last few, and wrote better than many who finished first.. You can still remember stuff and write it right..
You could also talk to your prof. about any grading procedures, and suggest what could be an improvement.. Maybe they just want to make sure that it's transparent, or for students to develop grading skills too? Or just don't think this could be a problem.. If you're generally nice (and unproblematic) maye some of your ideas will be listened to... (ideally in private and not when in a rush)
Even if you're late you can probably still take a test, perhaps later on privately.. or stay and write in the break.. depends on the prof. Or maybe you can finish in the time that remains anyway.. (some tests are short)
In our class, we sang 'Always look at the bright side of life' before tests
(Just the chorus.) It seemed to help!