We have performed for the first time precision spectroscopy on a coasting fast 7Li+ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (A-system). One laser was frequency locked to the a 3 127j 2 hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over the A-resonance, which was recorded relative to 127j 2 hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.