Yes, you should be able to do this with a workflow. You can use the Access Request Decision trigger to kick off the workflow. Setup a trigger filter to only activate the workflow if the requested item is a role or access profile and it was approved. You can then use the HTTP Action to send a request to Jira to create a ticket with the necessary details.
If you’re new to these things, I highly recommend you signup for developer days. On day 3 I will be demonstrating the various capabilities of event triggers and workflows which will help you understand how to achieve a use case like this.
The links I supplied in my response above are the technical docs that cover workflows. I’d start there and read everything. Then start playing around with workflows to get comfortable with it. And, of course, join my session next week to see a live demo.