Lets say a nation around this timeline was making research and advancements in firearms. Other than a flintlock or breech-loader, is it possible for them to produce a repeating bolt-action rifle? Would this require an industrial revolution to happen?
I hope it is simple as well as sufficient to say that the 'modern' centerfire rifle ammunition - nevermind the mechanism that the firearm uses, is a product of mass-production era post-industrial revolution. The cartridge needed for any contemporary firearm wasn't popular for this exact reason until around the American Civil War, c.1850.
Handmade examples or powder/projectile cartridges existed prior to the 1800s, but any bolt/lever/semi-auto or other "repeating" rifle will use ammunition at a rate that was mostly cost-prohibitive until Henry Ford's day. In short, I feel certain that the mechanism of the rifle would be far overshadowed by the lack of ammunition, especially in post-renaissance Europe.