Tough to include bad gag that's thin (7)
I believe the answer is:
haggard
'thin' is the definition.
(similar in meaning)
'tough to include bad gag' is the wordplay.
'tough' becomes 'hard' (similar in meaning).
'to include' means one lot of letters goes inside another.
'bad' indicates an anagram.
'gag' with letters rearranged gives 'gga'.
'hard' placed around 'gga' is 'HAGGARD'.
'that's' is the link.
(Other definitions for haggard that I've seen before include "Drawn, gaunt" , "She came from him" , "looking emaciated" , "Farm building for storing crops" , "Looking tired and unwell" .)