First try to identify exactly where the noise is coming from. Is it from the string being too close to a fret? Is it a rattling spring or other part from the tremelo setup? Is it a rattling tuner?
Once you know this you can tackle the problem.
If it's fret buzz you can raise the action by raising that end of the floating bridge via the allen screw in the post. Also heaving gauge strings will increase string tension and reduce fret buzz.
If you have a trusted local guitar luthier that is also an option.
Good luck!
