Local caving clubs are called grottos. There are several grottos throughout Texas that hold meetings, organize trips, offer training, and provide a general outlet for all things related to caving, cave research, and cave conservancy. Everyone interested in caving in Texas is encouraged to get involved by joining their closest grotto.
Austin
Underground Texas Grotto
http://utgrotto.org/
Facebook page
College Station
Aggie Speleological Society
https://cavetamu.com/
Facebook page
Dallas/Forth Worth
DFW Grotto
https://www.dfwgrotto.org
Facebook page
Houston
Greater Houston Grotto
Facebook page
Lubbock
Lubbock Area Grotto
http://lubbockareagrotto.org
Facebook page
Midland/Odessa
Permian Basin Speleological Society
Facebook page
San Antonio
Bexar Grotto
https://bexargrotto.org
Facebook page