Straight answer - in the normal sense, no authority whatsoever.
As Capot says, ICAO publishes SARPs in annexes. These documents are annexes to the 'Chicago Convention'. The States that sign the convention commit to give effect to the convention and the annexes. In most cases this is done by incorporating the ICAO measures into the national law - there are other ways to make the SARPs mandatory but ICAO likes the transposition into law method.
Again, and as Capot describes so beautifully and accurately in the case of Europe, groups of States may, make their own agreements about how to give effect to ICAO, and these agreements may have some form of supra-authority. This is what EASA is for Europe, although the enforcement mechanism soon goes 'above' EASA.
You might want to take a look at the ICAO Universal Safety Oversight Audit Programme (USOAP). This programme audited States for implementation of the convention and some of the reports have been published in the past, but they have been well hidden on the ICAO website. The programme has changed now (to more of a monitoring activity), but may still be of interest. There was no real 'power' in the USOAP report but it was seen as a way to name and shame recalcitrant States....and there were a couple of surprising names higher up the list than you might expect!
Last point is that it is the State that signs up to the Convention, not the CAA. Usually the CAA is just the way that the States decides to make it all happen in accordance with the SARPs etc., and so there may be directions to the CAA from Government to consider also.