Tracking Area update procedure is used by MME to track the UE at the granularity of tracking area(s). During attach or TAU procedure, MME assigns a list of tracking areas to UE. There are two ways to execute the tracking area update procedure. One way is known as periodic TAU and the other one is known as non-periodic TAU.
Now coming to your question, please find my inputs as following:
Tracking Area update procedure is triggered only when UE is in RRC-IDLE state. So it means, when UE has radio connection with eNodeB, there is no need to execute this procedure since MME is already aware about the location of UE at the cell level.
In RRC- IDLE state, when UE moves from current cell to other cell and the other cell broadcasting a tracking area which is not present in the TAI list, UE initiates tracking area update procedure.
Hope, now it is clear to you when the tracking area update procedure is executed.