Edited: SuiTest is now named TestFLO
SuiTest uses many JIRA built-in mechanism. There are issue types for test plan and test cases. If you want for example trigger a built of environment when test plan is started probably you should think about doing that with post-function.
In other hand, if you want to update test plan's field with some value (or change status to "Ready to test" if build is finished) you can use JIRA REST API.
You can also check webhooks https://developer.atlassian.com/display/JIRADEV/JIRA+Webhooks+Overview
There is no SuiTest API simply because it integrates with JIRA mechanism.