Gaga was joined by her boyfriend Christian Carino at the bash, which was held at LA's The Village, reported Us Weekly.
"They also shared a kiss during the party," a source said about Gaga and Carino, who first stepped out together this past February after the "Bad Romance" hitmaker split from fiance Taylor Kinney in July.
In "A Star Is Born", a remake of the original 1937 film, Gaga plays a small-town girl hoping to make it big, while Cooper, who is making his directorial debut with the film, plays an alcoholic has-been rock star who helps to advance Gaga's character's career.
The wrap party marked a night out for Cooper and Shayk, who welcomed their first child together, daughter Lea De Seine Shayk Cooper, in April.
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