Wife in test regularly displays brainpower (4)
I believe the answer is:
wits
'brainpower' is the definition.
(I've seen this in another clue)
'wife in test regularly' is the wordplay.
'wife' becomes 'w' (abbreviation).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'in'+'test'='intest'
The alternate letters of 'intest' are 'its'.
'w'+'its'='WITS'
'displays' is the link.
(Other definitions for wits that I've seen before include "Keep them about you to stay alert" , "They express themselves humorously" , "Mental faculties" , "Humorous people" , "Intelligence" .)