We present a multiwavelength study of the AGN-host starburst galaxy PKS 0529-549 at z \simeq 2.6 . We use ( 1 ) new ALMA observations of the dust continuum and of the [ C I ] 370 \mu m line , tracing molecular gas , ( 2 ) SINFONI spectroscopy of the [ O III ] 5007 Å line , tracing ionized gas , and ( 3 ) ATCA radio continuum images , tracing synchrotron emission . Both [ C I ] and [ O III ] show regular velocity gradients , but their systemic velocities and position angles differ by \sim 300 \mathrm { km } \mathrm { s } ^ { -1 } and \sim 30 ^ { \circ } , respectively . The [ C I ] is consistent with a rotating disc , aligned with the dust and stellar continuum , while the [ O III ] likely traces an outflow , aligned with two AGN-driven radio lobes . We model the [ C I ] cube using 3D disc models , which give best-fit rotation velocities V _ { rot } \simeq 310 \mathrm { km } \mathrm { s } ^ { -1 } and velocity dispersions \sigma _ { V } \lesssim 30 \mathrm { km } \mathrm { s } ^ { -1 } . Hence , the [ C I ] disc has V _ { rot } / \sigma _ { V } \gtrsim 10 and is not particularly turbulent , similar to local galaxy discs . The dynamical mass ( \sim 10 ^ { 11 } M _ { \odot } ) is comparable to the baryonic mass within the errors . This suggests that baryons dominate the inner galaxy dynamics , similar to massive galaxies at z \simeq 0 . Remarkably , PKS 0529-549 lies on the local baryonic Tully-Fisher relation , indicating that at least some massive galaxies are already in place and kinematically relaxed at z \simeq 2.6 . This work highlights the potential of the [ C I ] line to trace galaxy dynamics at high z , as well as the importance of multiwavelength data to interpret gas kinematics .