If you are extending a 'grandfathered' dryer or range line, where the neutral is serving double duty as the EGC, then you are an less solid ground.
The NEC 'wants' all of these circuits replaced, but has only limited ability to force such replacement. Some would argue that an extension is a sufficient change to no longer be considered a repair of an existing circuit, and that you need a new home run. Others would argue that the circuit exists and that an extension is still using the existing _grandfathered_ circuit.
I won't take sides on the issue; contact your AHJ.
If this is a 'proper' code compliant circuit, with separate neutral and ground, then there is absolutely no issue with splicing these conductors in a proper accessible junction box.
-Jon