I'm not aware of a TT plug-in for this, but it's trivial to add a line or two to your back-end application to make the information available to the template. For example, if your app is Catalyst based, you would add something like this to your main program:
__PACKAGE__->apply_request_class_roles(qw/
Catalyst::TraitFor::Request::BrowserDetect
/);
... and in your 'auto' handler, introduce a line such as (untested):
$c->stash(browser => $c->req->browser);
... or just use this is your template:
[%- SET browser = c.req.browser;
SET old_ie = 'class="old-ie"'
IF browser.windows && browser.ie && browser.public_major < 9.0;
-%]
and then include old_ie
wherever it's required in your template.
See Catalyst::TraitFor::Request::BrowserDetect and HTTP::BrowserDetect for more info and options. I'm sure there are similar plugins/methods for Dancer, Mojolicious etc.