The fathead is convinced there’s a crack (7)
I believe the answer is:
fissure
'a crack' is the definition.
('fissure' can be a synonym of 'crack')
'the fathead is convinced' is the wordplay.
'the fathead' becomes 'f' (head letter of 'fat').
'convinced' becomes 'sure' ('sure' can be similar in meaning to 'convinced').
'f'+'is'+'sure'='FISSURE'
'there's' is the link.
(Other definitions for fissure that I've seen before include "Cleft" , "Crevice" , "Split - cleavage" , "Deep crack in rock" , "Long, narrow crack" .)