You can have your zimlet create an app (i.e. a tab) in the zimbra web client. Check out this example:
ZCS 6.0:Zimlet Developers Guide:Examples:Simple Tab - Zimbra :: Wiki
The tab method hooks on the zimlet base JavaScript class are described in this JsDoc:
Zimlet JavaScript API Reference - ZmZimletBase
And here is an illustration of when those tab method hooks are called:
ZCS 6.0:Zimlet Developers Guide
eveloping Zimlets - Zimbra :: Wiki