TAPIS is a 5 letter word that starts with T.

1. \Ta"pis\, n. [F. See {Tapestry}.]
   Tapestry; formerly, the cover of a council table.
   
   {On}, or {Upon}, {the tapis}, on the table, or under
      consideration; as, to lay a motion in Parliament on the
      tapis.
   
   

2. \Tap"is\, v. t.
   To cover or work with figures like tapestry. [R.] --Holland.