The White House said earlier this year it would end direct funding of the orbiting outpost by 2025, a position that raised fierce opposition among some lawmakers.
The livestream above, courtesy of NASA TV's public streaming service, began coverage at 11.15pm BST straight from the Kazakhstani Cosmodrome.
The space agency plans to live-stream the docking process and also show the astronauts moving from the spacecraft to the ISS to join the current crew: Americans Drew Feustel and Ricky Arnold, and Latvian Oleg Artemyev.
The three astronauts returned safely to Earth on June 3 in a parachute-assisted landing on the steppes of Kazakhstan.
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The crew will spend more than five months conducting about 250 science investigations in fields such as biology, Earth science, human research, physical sciences and technology development.
The crew will have to perform 55 scientific experiments during their mission, as well as head into outer space, carry out maintenance work and shoot videos. A flight surgeon, she previously had been in Russian Federation supporting medical operations for International Space Station crew members in Star City.
The capsule has already made several trips to and from the space station, taking supplies and other cargo.
A majority of Americans say NASA should remain a global leader in space exploration, but a recent Pew Research study looking at the public's perception of the USA space program find support for a human mission to the moon or Mars is low. Pew Research Center asked survey participants to rate the importance of the following nine missions.