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A heavenly body revolves around a massiv...

A heavenly body revolves around a massive star in a highly elliptical orbit..Is its angular momentum constant over the entire orbit?

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Yes, angular momentum remains constant over the entire orbit. When a planet revolves around a massive star, the gravitational force between them acts along the line joining planet and the star, angular component of the force `(F_theta)` will be zero.
Torque acting on the revolving planet,
`tau= tau F_theta" "implies " "tau = 0 " "[:. F_theta=0] `
Also = `(dL)/(dt)=tau " or " (dL)/(dt) = 0`
`implies ` L = constant.
Hence, angular momentum remains constant.
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