Shabby hat worn by that man (5)
I believe the answer is:
cheap
'shabby' is the definition.
(thesaurus)
'hat worn by that man' is the wordplay.
'hat' becomes 'cap' (cap is a type of hat).
'worn by' means one lot of letters goes inside another (outside letters are worn by those on the inside).
'that man' becomes 'he' (he refers to a man).
'cap' placed around 'he' is 'CHEAP'.
(Other definitions for cheap that I've seen before include "Vulgar" , "A snip" , "Second-rate" , "good value" , "Economical - rubbishy" .)