There is only one file type that uses the .TIGER extension:
Tomb Raider Game Data Archive
A TIGER file is an archive consisting of game data used by Tomb Raider (2013), Rise of the Tomb Raider (2015), or Shadow of the Tomb Raider (2018). It contains sound effects, music, models, textures, and other files used by the game.
Tomb Raider is packed into four large TIGER files that contain all of the data in the game. In order to access the contents of these files they must first be unpacked, which can be done using Gibbed Tiger Unpacker.
NOTE: TIGER files should be backed up before modifying them.
Updated: September 9, 2020