Angle to go round beat regularly -- it's an obsession (6)
I believe the answer is:
fetish
'an obsession' is the definition.
(thesaurus)
'angle to go round beat regularly' is the wordplay.
'angle' becomes 'fish' ('fish' can be a synonym of 'angle').
'to go round' means one lot of letters goes inside another.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternate letters of 'beat' are 'et'.
'fish' placed around 'et' is 'FETISH'.
'it's' acts as a link.
(Other definitions for fetish that I've seen before include "charm" , "Object worshipped by primitive people or fixation (6)" , "magical object" , "Object worshipped as having a spirit" , "Object worshipped by primitive people or of abnormal sexual interest" .)