Fatty regularly said "I am a model" (7)
I believe the answer is:
adipose
'fatty' is the definition.
('adipose' can be a synonym of 'fatty')
'regularly said i am a model' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'i am' becomes 'i' (I've seen this in other clues).
'a model' becomes 'pose' (I've seen this before**).
The alternating letters of 'said' are 'ad'.
'ad'+'i'+'pose'='ADIPOSE'
(Other definitions for adipose that I've seen before include "Relating to fat" , "Is a dope fat?" , "Fat-storing (tissue)" , "Obese" , "Of animal, fat, fatty" .)