What type of competition shooting? There are quite a few.
A good competition for folks new to it are the
American Action Shooting Association (AASA) matches at A place to shoot on the 2nd and 4th Saturdays. Third Saturday matches are held at Lone Star Handgun. If there's a 5th Saturday, there's a 3-Gun match at LoneStar Handgun. Ted Bonnet, who was a world champion in the 90's, encourages new shooters and often gives a bit of coaching during the match.
There are IDPA, USPSA, Steel, and self defense matches at
Cedar Ridge Range
There is a
USPSA and Steel Challenge match at Black Hawk Range.
NRL22 match at Bexar Community Shooting Range
The easiest way to find local matches is to use
Practiscore
Due to ranges closing and the high cost of putting (labor, props, facilities) on a match, most of the 3gun matches in the area have shut down.
I usually shoot the Alpha Mike USPSA match in Cedar Ridge and 1st and 3rd Saturday Austin Practical Shooting Club USPSA match. I'll try and catch an AASA or a steel match at Cedar Ridge on occasion, they're fun, friendly and good for new shooters. I try to shoot NRL22 matches but it conflicts with Alpha Mike - perhaps after the competition season ends for me in November.