Generally, the web application is part of the service which
encompasses the web server and directory service. They should
already have an appropriate trust relationship.
BTW: This is a very broad assumption not valid in all deployments.
Nevertheless it's always good practice to avoid overly powerful system
components since in this case the web application could have security
problems.
Kerberos with forwardable tickets could be a solution. One could argue
that as a forwardable ticket is a full TGT you also have to trust the
web application a little bit more. But given the limited lifetime of
TGTs the risk is significantly lower than long-time service credentials
for the web application together with the right for doing proxy
authorization.