If you replace the display your self, Face ID and True Tone will no longer work (Yet another one of Apple’s attempts to deter people from doing it themselves, and paying them high prices do to it instead.) This is because the parts in your phone are paired via serial numbers, meaning removing the original display and replacing it with another one will cause the features associated with that specific part of your device to be unusable. The display and front camera will function normally but you will frequently be reminded by your phone that the display is not a genuine Apple display.
There is however there is a work around, using a machine similar to a QianLi iCopy, it is possible to copy the original serial number from the display and put it on your new display, tricking the phone into thinking the new display is the original, meaning Face ID, and true tone will function normally.
In short, I would personally fix it myself and use a machine to reprogram the screen making it function normally. If you are not interested in doing the above then I would recommend checking with a repair shop and getting a quote from them, before taking it to Apple and paying top dollar for an relatively easy fix.