There already is an in-game clock in your GUI - you can set the clock in the top right corner of the screen (the one next to the connection icon and above the mini-map) by simply clicking on it to display either 'Local Time' (which is based on your computer/console's clock setting), 'Eorzean Time' (which is the in-universe time that you are after), and 'Server Time' (which I understand is based on GMT).

This clock doesn't display in-game month and year like the FFXI version did however, but I guess SE must have considered that not worth incorporating as it has pretty much no impact on actual gameplay at this stage.