Data Validation in cell X depending upon the value in cell Y?

I have a worksheet with a list of teams: A, B, C, etc and in cell a1 I have data validation set to that list, so that the team names can be picked from a drop-down

I then have separate lists for the name of people in each team. E.g:
Team A has a list containing alice, bill, george, etc
Team B has a list containing brian, dave, sue, etc
:
:

What I'd like is,
if I select Team A in cell a1, to be able to have JUST Team A's list available from the drop down in cell b1.
but if I select Team B in cell a1, to be able to have JUST Team B's list available from the drop-down in b1
ETC, Etc, etc ...

Any ideas how this might best be achieved, please?