Question

how does ATP enable transport proteins to move ions across a cell membrane?

Answer 1

@esshotwired I don't think they ask for that, but that transport proteins that require ATP gets phosphorylated which cause the protein to change conformation which allow the specific ions to move across the membrane.
Consider the mechanism of Na/K-ATPase as an example (a P-type ATPase).

Answer 2

Another example could be the sarcoplasmic/endoplasmic reticulum \(\sf Ca^{2+}\) ATPase pump (also known as the SERCA pump).