Turkish is a member of Star Alliance, which is celebrating its 15th year, and the livery is a Star Alliance livery. What does this have to do with when Turkish joined SA or how long they have been a member?
For example:
Brussels Airlines has been a member of SA since 1999, it also has the 15 years SA livery.
Ethiopian Airlines has been a member of SA since 2011, it also has the 15 years SA livery.
Perhaps a better sentence would be "They now have a sticker on few of their aircraft to promote 15 years of Star Alliance, of which the airline has been a member of since 2008..."