If you've sanded back the original finish and properly applied a new satin finish, then there's no need for another finish. It all depends on the finish you've applied, how many coats you've applied, what kind of finish you're hoping to achieve and how well the new finish went on as to whether you need to do more on it. But you'll be the one that knows if the finish looks right or not. It's difficult to comment any further without a bit more detailed info (pictures ideally)of what you've already done.
Jim
thx Jim, i applied like this: primer - 2 coats, black satin paint from a can - 3 coats. at the actual moment the paint is still drying, i put the last coat on feb 8. i thought it will be not to good with 3 coats, but it is very good, better than i expected . the problem is not how i want, i know that, but rather is the satin finish needs to be protected or not with a clear coat?? this is the question that i`ve been asking myself. I have some pictures, but don`t know how to post them in here...