Board under pressure to exercise authority (7)
I believe the answer is:
preside
'to exercise authority' is the definition.
I can't judge whether this defines the answer.
'board under pressure' is the wordplay.
'board' becomes 'reside' (board can mean to stay in an establishment).
'under' says to put letters next to each other (below, in a down clue).
'pressure' becomes 'p' (abbreviation).
'reside' after 'p' is 'PRESIDE'.
Can you help me to learn more?
(Other definitions for preside that I've seen before include "Be chairman" , "Be in authority (over)" , "Take the chair" .)