Thing that is regularly what ballet dancers wear (6)
I believe the answer is:
tights
'what ballet dancers wear' is the definition.
'thing that is regularly' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'thing'+'that'+'is'='thingthatis'
The alternate letters of 'thingthatis' are 'TIGHTS'.
(Other definitions for tights that I've seen before include "Hose coverings from waist to feet" , "Nether garments for women or acrobats (6)" , "Woman's garment" , "Close fitting garment" , "form of legwear" .)