When she starts climbing, the tension in the rope is greater than when she hangs stationary.
Work Step by Step
When the circus performer hangs stationary from a rope, she is under the influence of her own weight $mg$ which points downward and the tension in the rope $T$ which points upward. Being stationary means there is no acceleration, so $$T=mg$$ When she starts climbing upward, she is still under the influence of the same 2 forces but now she has an upward acceleration $a$. According to Newton's 2nd law, we have $$T-mg=ma$$ $$T=m(g+a)$$ which is greater than $T$ when the performer is stationary. Therefore, when she starts climbing, the tension in the rope is greater than when she hangs stationary.