For a standard booking, you cannot change your TUI flight for free and will likely have to pay an amendment fee plus any difference in fare. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) Free changes are possible only if you purchased the add-on called TUI Flex, or if TUI cancels or significantly alters your flight. 

Conditions for free flight changes

• If TUI cancels your flight: You are entitled to a full refund or can change your booking without an amendment fee.
• If TUI makes a major change: If your flight is significantly altered—such as a change in destination, a lower category of accommodation, a flight time change of more than 12 hours, or a UK departure airport change—you can cancel for a full refund or accept new arrangements. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) This does not apply if the change is caused by events outside TUI's control.
• If you purchased TUI Flex: This optional extra allows you to make a single fee-free change to your date, destination, or passenger name up to 28 days before you travel. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) You will still be responsible for paying any increase in the holiday price, and the TUI Flex fee itself is non-refundable if you cancel.