How might the "Convention against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment" be applied to a contemporary conflict?

When you say "applied to" I assume you are not asking
about how it could be enforced.  Instead, I assume that you are asking how the
convention applies to or is relevant to a given
conflict.

One of the provisions of the convention is a
definition of torture.  One part of the definition is that torture includes any
action

...by
which severe pain or suffering, whether physical or mental, is intentionally inflicted
on a person for such purposes as ... intimidating or coercing him or a third
person...

One way in which
this aspect of the convention is violated is the use of rape as a weapon of war.  As the
economist.com link below shows us, rape has come to be used systematically to coerce and
intimidate opponents in the various conflicts in African countries today.  This is
surely a case in which the convention applies, even though it would be extremely
difficult to try to enforce it.