I would assign it a due date so it shows up on my calendar. By setting a due date on the task this means it is the date I want to have it done by to be sure I'll meet my agreed timelines with others.
I differentiate between due dates and deadlines, deadlines are committments I have agreed to with others, and there will be people chasing me up if I don't meet them or renegotiate them. I set deadlines separately, I have created a deadline context, so all get added there. Deadlines are not actions, I don't do a deadline, it is in my system so I can review it, but I have separate next actions to actually meet them. I also know I can't change a deadline unless I discuss and get agreement with others.
I can change my due dates myself without having to ask someone. However I know I set the due date for a reason, ie to meet the project plan or deadline, so I like to check the project plan before giving myself an extension, and make sure it'll still be ok. Although be warned, your calendar is sacred space and don't give due dates to too many tasks, only those that really are top priority, otherwise you'll just end up making a daily to-do list and never get to work off your lists.