Transition_linkedIssue.groovy

import com.atlassian.jira.component.ComponentAccessor
import com.atlassian.jira.workflow.IssueWorkflowManager

def issueManager = ComponentAccessor.issueManager
def issueService = ComponentAccessor.issueService
def issueWorkflowManager = ComponentAccessor.getComponent(IssueWorkflowManager)
def user = ComponentAccessor.jiraAuthenticationContext.loggedInUser

def customFieldManager = ComponentAccessor.getCustomFieldManager()
def parentLink = customFieldManager.getCustomFieldObjectByName('Parent Link')

def customFieldValue = issue.getCustomFieldValue(parentLink)
def parentKey = customFieldValue.key
def parentIssue = issueManager.getIssueByCurrentKey(parentKey)
def startProgressAction = issueWorkflowManager.getAvailableActions(issue, user).find{it.name == "Start Progress"}
def inputParams = issueService.newIssueInputParameters()
def validationResult = issueService.validateTransition(user, parentIssue.id, startProgressAction.id, inputParams)
if (validationResult.valid) {
 def issueResult = issueService.transition(user, validationResult)
 if (issueResult.valid) {
 log.debug "Successfully transitioned $parentIssue.key"
 } else {
 log.error("Could not transistion $parentIssue.key to in progress following $issue.key")
 log.error(issueResult.errorCollection?.errorMessages)
 log.error(issueResult.warningCollection?.warnings)
 }
} else {
 log.error("Could not transistion $parentIssue.key to in progress following $issue.key")
 log.error(validationResult.errorCollection?.errorMessages)
 log.error(validationResult.warningCollection?.warnings)
}

Issue workflow manager is important to use, instead of hard-coding transition ids
def startProgressAction = issueWorkflowManager.getAvailableActions(issue, user).find{it.name == "Start Progress"}