Yes, both Jira and DeskTime offer a Free Trial.
Jira is designed for Large Enterprises, Medium Business and Small Business.
DeskTime is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
Pricing for Jira Starts at $6.25/User/Month when Billed Yearly whereas for DeskTime Starts at $87.08/Month when Billed Yearly.
Some top alternatives to Jira includes Trello, Confluence, Asana, SwiftKanban, Kanbanize, ClickUp, Height, Kanban Tool, Kanban Zone and KanbanFlow.
Some top alternatives to DeskTime includes clockodo, Time Doctor, TimeTracker App, Hubstaff, TrackingTime, Clockify, TimeTrack, Time Track Bill, Timesheet and Time Analytics.