Regularly arouse regret (3)

I believe the answer is:
rue
'regret' is the definition.
(to rue something is to regret it)
'regularly arouse' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternate letters of 'arouse' are 'RUE'.
(Other definitions for rue that I've seen before include "The 'herb of grace'" , "Be regretful" , "Regret in a French street" , "show you're sorry!" , "Deplore" .)