How much clearance do I need between floating ground and earth referenced ground?
Do I need to have clearance between two grounds to avoid hazard or arc?


Yes. Is suspect this is functional isolation required for the operation of the device, but not to protect users from shock.


  Since both points are concealed within a metal cover which are grounded, do I need to follow the clearance requirement as required by the safety standard?


You need to comply to the relevant standard. They will have requirements with a test scenario for the isolation barrier. 

Eg: 50178:1997 (A.9.4.6.5)
- insulation resistance: 100 MΩ;
- dielectric strength: a.c. 1 kV or d.c. 1,5 kV (60 s duration);
- pulse withstand: 1,2/50 ms, 2 kV (peak value)  

Even if the standards are not a requirement, use them as guideline.



If it is safety isolation then all of the above is invalid, the standards are mandatory and significant distances and strict requirements on parts apply. And have your device tested by a certified auditor.