Tommy Lee Jones portrays the very elusive and mysterious businessman Clay Shaw who in the film seems to have some involvement with the assassination of JFK although it never says precisely what his association is. Tommy Lee Jones portrays Shaw in an equally mysterious fashion, and although Stone is not a subtle director by any means there is most certainly subtly laced within Jones's work in this film.
Jones role is in the end quite small really. Much of his appearances in scenes are only very very short moments that merely indicate his presence more than anything else. Nevertheless Jones still creates compelling character within these short scenes. Jones never for a moment exactly says who Shaw is in but rather creates him into a fascinating enigma that is basically impossible to fully understand. An enigma is actually quite a difficult role to find the right balance as it is easy to give away too much of the character or too little that it just seems like thin characterization. Jones though manages to find the perfect balance of the known and unknown in his performance. There is an underlying sinister quality to Jones' portrayal that is always clear and chilling in an understated way but mysterious by the way Jones never exactly say what makes Shaw so sinister.
Jones gives a careful but concise performance that always seems to suggest the Shaw is hiding something, but Jones is good enough that he is able to convey in small indications that he is hiding something, but at the same he is able to show that Shaw is exceedingly good at hiding his secrets. This again something that is very difficult to convey but Jones is masterful in portraying that here. Jones's role is quite short but you do actually feel his presence almost throughout the film from the his short time. I really do not like to use that overused phrase with performances, but it is true of Jones's work here that absolutely creates fascinating character who acts as the incarnation basically of the conspiracy in the film.