... a query to update each staffname ...
I am not sure is yo want ro add (insert/append query) the skill or update an existing record.
If ass the skill to the staff when why add the records?
If the record not not exist would mean "Not_Evaluated" for that skill? If yes, then I would not add the records. I would calculate this as needed.
Also you tbl1 ( staffname, mgrname, skill, skillLevel) has some data normalization issues. This really needs addressed before going forward. Once htios is fixed, adding a skill will be much easier.