As I understand it, from what I read somewhere, recourse to the Swiss court can only be made on the basis of technical/procedural flaws during the CAS case, not the substance of the case itself. I'm open to correction but if this is right, then anyone holding out hoped for a further appeal except on procedural irregularities can forget it.
There seems to be unsurprisingly a lot of speculation on here about CAS and Swiss courts. For those interested (and please don't let this get in the way of a good rant) the CAS website has a handy FAQ section:
https://www.tas-cas.org/en/general-information/frequently-asked-questions.html#c198
For those insufficiently arsed to read through this, the following two extracts might be useful in the context of some previous posts:
How long does CAS arbitration last ?
The ordinary procedure lasts between 6 and 12 months.
For the appeals procedure, [City's case as I understand it] an award must be pronounced within three months after the transfer of the file to the Panel.
In urgent cases and upon request, the CAS may, within a very short time, order interim measures or suspend the execution of a decision appealed against.
Is it possible to appeal against a CAS award ?
Judicial recourse to the Swiss Federal Tribunal [Switzerland's Supreme Court I believe] is allowed on a very limited number of grounds, such as lack of jurisdiction, violation of elementary procedural rules (e.g. violation of the right to a fair hearing) or incompatibility with public policy.