Examine popular party holding power (7)
I believe the answer is:
inspect
'examine' is the definition.
(inspecting is a kind of examining)
'popular party holding power' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'party' becomes 'sect' (I've seen this before).
'holding' means one lot of letters goes inside another.
'power' becomes 'p'.
'sect' enclosing 'p' is 'spect'.
'in'+'spect'='INSPECT'
(Other definitions for inspect that I've seen before include "test" , "Go over" , "Study" , "Look over carefully" , "Carefully examine" .)