Are you using Lightning Data Service?
If you use Lightning Data Service (force:recordData) The utility bar component will pick up change.
From Salesforce Docs,
Records loaded in Lightning Data Service are cached and shared across
components. Components accessing the same record see significant
performance improvements, because a record is loaded only once, no
matter how many components are using it. Shared records also improve
user interface consistency. When one component updates a record, the
other components using it are notified, and in most cases, refresh
Set "recordUpdated" attribute with an action, Then in that action logic, handle refresh view logic.
Example @ here
@AjaySFDC @tsalb I think, we can use
Place it in your Component housed in UtilityBar.
Then, Use onUtilityClick() Method of utilityBarAPI which should register an event handler for Utility click. You can call doInit in that eventHandler logic.
The above links should help you implement this.
Let me know if it fixes the issue or Did i get it wrong again?