Rising star will not help to get more connects. If you need more connects, you have to take the "Plus Membership" Plan.
To do it, go to
Click on "Membership and Connects"
Click on "View or edit membership plan"
Click on "Upgrade" button on the right top on the "Plus" section.
Remember, it will cost you $10 for a month.
You will get 10 extra connects and will get back all rollover connects up to 140 connects. Ok, you will get all the info there.
Hope it solves your problem.
I read this and it clearly says that if you become rising star you will get 30 connects for free once. Am I mistaken somewhere this is taken from an official Upwork site. Program Perks
As a Rising Talent, you receive the following perks:
Rising Talent status is automatically applied to users who's profiles meet all of the requirements. You can have a look at this article about Becoming Rising Talent to see what the exact requirements are that you must meet to obtain a Rising Talent badge on your profile. Once the requirements are met, you'll be invited into the program automatically and receive the badge and 30 free connects within 48 hours.