Regularly visit sleazier den (4)
I believe the answer is:
lair
'den' is the definition.
(synonyms)
'regularly visit sleazier' is the wordplay.
'regularly visit' means one should take alternating letters (I've seen 'regularly visited' mean this (letters are taken at regular intervals)).
The alternate letters of 'sleazier' are 'LAIR'.
(Other definitions for lair that I've seen before include "Habitation of a wild animal" , "Study" , "Rail around hiding-place" , "Rail around animal's den" , "Wild animal's den" .)