White House deputy turned up European bug (5)
I believe the answer is:
peeve
'bug' is the definition.
(both can mean to annoy)
'white house deputy turned up european' is the wordplay.
'white house deputy' becomes 'veep' (VP, vice president).
'turned up' says the letters should be written in reverse.
'european' becomes 'E' (abbreviation e.g. EU).
'veep' back-to-front is 'peev'.
'peev'+'e'='PEEVE'
(Other definitions for peeve that I've seen before include "Cause to be annoyed, irritated, or resentful" , "Vex" , "bug" , "Cause resentment" , "Get annoyed" .)