UE triggers tracking area update procedure to report its location to MME at the granularity of tracking area.
In the connected mode (EMM-REGISTERED, ECM-CONNECTED and RRC-CONNECTED) , MME knows the current location of an UE at the cell and a tracking area level but when the UE moves from connected to Idle mode (EMM-REGISTERED, ECM-IDLE and RRC-IDLE) mode, MME tracks the UE based on the tracking area identity (TAI) list, this is the list MME sends to UE in the attach accept or tracking area update accept message.
Assuming UE is in idle mode and found an another cell that has better signal strength and performed cell re-selection.
Since the new cell belongs to different tracking area that is not the part of TAI list assigned to UE, tracking area update procedure is initiated by UE to network.
In tracking are update request message, UE sends old GUTI and it may get new GUTI from MME in TAU accept message.
When UE gets new GTUI in TAU accept message and it acknowledges to MME by using the TAU complete message.
The same information is captured in 24.301 spec. Please have a look and still you have any doubt then send me the message.