In my experience as an American English speaker, there is no single word to describe this in general. If the context is specifically periods between work in a workday, I’d use “break”.
“I have a break between lessons/meetings from 10 to 10:30.”
“My lunch break is from noon to 1 pm.”
If I am going to have time at a station or airport before some trip, I would say, “I’ll have thirty minutes before the flight/the train”.
“Down time” exists in US English, but I personally never hear it used for *short* periods between other activities.