Doubts persist regularly and dominate (6)
I believe the answer is:
obsess
'dominate' is the definition.
(thesaurus)
'doubts persist regularly' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'doubts'+'persist'='doubtspersist'
The alternate letters of 'doubtspersist' are 'OBSESS'.
'and' acts as a link.
(Other definitions for obsess that I've seen before include "Haunt - preoccupy" , "Be constantly talking about" , "Bosses (anag.)" , "Think only" , "Occupy the thoughts persistently" .)