There are lots of replies to similar questions on this forum about PI delegation & delegation logs.

My understanding is that the PI takes total responsibility for the trial at an investigator site. That is, he or she must perform all the protocol and GCP required tasks, unless the PI formally and proactively delegates some of those tasks to appropriately qualified, trained and experienced named staff. The PI at all times retains the overall responsibility for the trial and must supervise those individuals that he or she delegates. The PI should not allow staff who have not been delegated trial related tasks, to perform those tasks before they have been formally delegated. The PI will not know that the individuals have been suitably trained, if there is no documented evidence of that training having been completed before the task is delegated to them.

Your Risk Assessment could detail when staff are conducting routine activities that they are already trained and qualified for and because they are not performing a specific trial related task, hence they may not need trial related training. The MHRA GCP guide (2012) discussed about using a risk proportionate approach to training needs.