Getting on at this school? (8)
I believe the answer is:
Here is my best explanation:
This clue is a double definition.
'getting on' is the first definition.
('board' can be a synonym of 'get on')
'this school?' is the second definition.
(boarding school is a kind of school)
'at' is the link.
(Other definitions for boarding that I've seen before include "-- School; -- pass", "Staying at school", "public school arrangement", "getting on", "Getting on (a train)", "Sort of party" and "Embarkation".)