Tex. Ins. Code § 542.302

An insurer that brings suit or takes other action described by Section 542.202 against a responsible third party relating to a loss that is covered under a private passenger automobile insurance policy issued by the insurer and for which the responsible third party is uninsured is entitled to recover, in addition to payments made by the insurer or insured, the costs of bringing the suit or taking the action, including reasonable attorney's fees and court costs.