Persistently questions upper-class politicians under pressure (5)
I believe the answer is:
pumps
'persistently questions' is the definition.
(pump can mean to persistently question someone)
'upper-class politicians under pressure' is the wordplay.
'upper-class' becomes 'u' (similar in meaning).
'politicians' becomes 'MPs' (Members of Parliament).
'under' says to put letters next to each other (in a down clue, some letters go below others).
'pressure' becomes 'p' (abbreviation).
'u'+'mps'='umps'
'umps' after 'p' is 'PUMPS'.
(Other definitions for pumps that I've seen before include "Moves fluid or gas by pressure or suction" , "footwear" , "Mechanical devices that move fluid or gas" , "Cycle attachments" , "Water-raising devices" .)