TexasCHLforum.com

You're right. It is a trade off. If you get it before your birthday, you have to renew a year earlier. Renewals cost $70 and are good for 5 years, so by one calculation the down side to an early issue is $14. The up side to an an early issue depends on if you're in a situation before your birthday where you need to use your concealed handgun. (Assuming you don't have another state's license for reciprocity.)

I don't know if DPS is following the law but this is what the law says. (GC 411.183)

(a) A license issued under this subchapter expires on the first birthday of the license holder occurring after the fourth anniversary of the date of issuance.
(b) A renewed license expires on the license holder's birthdate, five years after the date of the expiration of the previous license.

Unless you're worried they will issue your CHL in less than two weeks, I say go ahead and apply now. You still have to mail your CHL-100 and photo, even if you applied online and did L1 fingerpaints, and the post office will add a few days to the process.

For renewals, there's no benefit to waiting because it expires 5 years after the previous one, even if you have a gap in coverage.