If you want to deny access to the system time, you’d pretty much have to write a system call filter; nowadays that would be a seccomp filter. See Kees Cook’s simple tutorial, or for more complex requirements, libseccomp. You’d need to deny access to
time, at least; the details depend on whether you’re trying to deal with an adversarial application (where you might also want to deny access to
system etc. to prevent an application from running external applications — although seccomp filters are inherited so that might not matter —, and deny access to external, direct or indirect time sources such as the network or even file systems).
If you want to give the application an artificial time, look at
faketime and libfaketime.