The only time HPD or any other law enforcement agency will (generally) take your Texas Driver License is if you refused consent to a blood draw. If they took your license it isn’t immediately suspended.
However, if you’re stopped by HCSO or HPD, and don’t have your license on you while driving, you’ll likely be taken to jail for identification purposes in which matters can only escalate for a negative end.
Your Texas Driver License isn’t officially suspended until you receive, by mail, an official letter titled “Notice of Suspension”. Once you get this notice you’ll have roughly 15 days to challenge the suspension via a process referred to as an ALR (Administrative License Revocation) hearing.
If you neglect to challenge the suspension of your driving privilege it will take effect within roughly 30-40 days of the date on the Notification of Suspension letter.