High level, two ways
1. Pull option . => You poll regularly from the Incident Management tool into Splunk (eg API of your tool, SOAP, directly Database etc.)
2. Push option . => The Tool can send the data to you (mostly HEC)
For option1, lot of incident management tools have addons (TA) for example ServiceNow Addon which can you just configure with credentials to pull information on regular basis.
There are other few as well apps too.
It would help if you said what incident management tool you use. If you don't find an app in splunkbase, you still have a few options:
1) Contact the vendor to see if they have an app for Splunk
2) Install a universal forwarder on the system hosting the IM software and forward logs/files to Splunk
3) Use the vendor's API to create a modular input to extract the information you desire
4) Use DB Connect to extract data from the IM system's SQL database.
--- If this reply helps you, an upvote would be appreciated.