Yes, they refer to this as a "detainer".
https://www.inmateaid.com/ask-the-inmate/if-you-have-a-hold-in-another-state-does-the-other-state-pick-you-up-after-you-serve-your-time-in-the-state-you-39-re-in.amp#answer
Accepted Answer Date Created: February 01,2018