Replace the tar once in sidewalk and drive? If so, how do I do this?
Background:  I live in Central Oklahoma, where summer highs are
routinely around and over 100 degrees and winter lows are often below
freezing.  The tar which once filled some of the seams of the walks
and drives around my house has largely fallen out.  Do I replace?

You don't say what materials your walk and drive are made out of and
that would determine a course of action.  There are several reasons to
have "TAR" in-between areas of pavement. One is to compensate for
expanstion and prevent cracking, another to help determine where the
cracking will be when it inevitably happens and the next is to
waterproof the joint.  You need to determine why the cracks were
sealed in the first place to answer the question.  Like any products
there are good, better and best quality filer/sealants.  You need to
decide what your situation requires. Is looks important? Do you want
to do it again in a few years?
are the areas of pavement moving?

I expect that the tar or asphalt is there to avoid water freezing to
ice in the cracks, which could  cause damage to the concrete.
I would ask a local expert.