What does "carry that beat" mean?

What does "carry that beat" mean?
This excerpt is from "pantaloon in black" by Faulkner:

"... And Mayfield trying to tell her what might happen maybe to her too if them Birdsong kin catches us before before we can get him locked up, only she is coming any way and, like Mayfield says, her being in the car might be a good thing if the Birdsongs did happen to run into us, because interference with the law can't be condoned even if the Birdsong connection did carry that beat for Mayfield last summer.

Would you please tell me what "carry that beat" means? Thank you.