The arrangement comprises a seal (500) sealing a cylindrical rotating part (100) passing through an opening in a support structure in the vessel (10) against a medium (W). The seal (500) comprises a package of annular seal rings (510, 520, 530). Each seal ring (510, 520, 530) comprises a seal part (512, 522, 532) being supported in a corresponding seal support part (511, 521, 531). The seal support part (511) in the first seal ring (510) positioned closest to the medium (W) has the form of a cylinder (511A) provided with an annular flange (511B) at one end of the cylinder (511A). The outer surface of the cylinder (511A) is supported and sealed with an auxiliary seal (610) against the inner circumference of the opening. The annular flange (511B) is supported against the support structure (83) surrounding the opening. There are adjusting means (900) for adjusting the position of the first seal support part (511) in relation to the support structure (83) surrounding the opening in order to relocate the seal (500) in an axial direction in relation to the rotating part (31, 100).