The phrase "to have the straps" means that someone is in control or in charge of a situation or project. It suggests that the person has the ability and authority to make decisions and direct others.
Sentences with «to have the straps»
Not only does it have the detachable strap that I love but it also has a strap on the outside flap that makes it that much easier to run around with. (fashiongrail.com)
I have a something similar to # 2 but they don't have the strap in the back. (bylaurenm.com)
It also has a strap so it can be worn on your shoulder. (ladyinviolet.com)