TimeAlignmentTimer is the duration when UE is considered as uplink synchronized. TimeAlignmentTimer is configurable at cell level as well as dedicated level i.e. UE specific. At the cell level timeAlignmentTimer is configured in SIB2 and at the UE level it is communicated within the MAC-MainConfig.
If UE receives Timing Advance Command from eNodeB, it restarts the timer again but if it does not receive any Timing Advance Cmd from eNodeB until expiry of timer, UE does RACH procedure again.
Please correct me if my understanding is incorrect.