You should contact the authority that issued your tourist visa rather than asking these questions on an online forum because they would know for sure. Any information you get online from a random stranger could be highly inaccurate and might land you in trouble.
I'll tell you what I think though, most countries I've been to issue 90 day tourist visas (even if you only go for 7 days) which is probably what you have, meaning you can enter at any date while it's still valid and stay for the full duration. As your visa for Cyprus would have to be issued by a Cypriot government body, not the UAE, you can most likely enter from a different country but there could be specifics stating that you have to come from there.
I have friends from Asia who are in Europe on student visas, and when they want to travel somewhere within Europe they have to apply for tourist visas and state the exact number of days they intend to stay. But this is different as they're already living in Europe on their student visas.
If you don't have a 90 day visa but in fact a 7 day visa you should get this extended with another 10 days before you go to Cyprus, just to save yourself the hassle of running around in a foreign country trying to find the right government office and spending your time here on this. Me and a friend once spent two days waiting outside the Russian embassy for something similar, so better to get it sorted before you go, even though that's a horror example

Although, if you want to extend a tourist visa I've never had a problem doing it once I'm in the country, it's only when you want to change your visa type that you have to exit, apply from abroad and then re-enter the country.
I'm an EU national though so I have an easier time than a lot of people I know from other places when it comes to these things, check with the Cypriot embassy instead.