The main impact of a three term limit on members of the Texas state legislature would not be on the members themselves. The main impact would be felt by the legislature as a whole, not by the individual members.
Individual members would, of course, be impacted. They would no longer be able to have long careers in the Texas House of Representatives. This would not likely be a tremendous blow to them, however. The Texas legislature does not meet full time and the pay is not very high. Therefore, most members must have other sources of income. Therefore, losing out on the ability to serve in the legislature would not be a huge blow.
However, term limits would have an impact on the legislature as a whole. There would no longer be legislators with long-term knowledge of the issues and of the process of making legislation. This would reduce the “institutional knowledge” that the legislators had. This would mean that legislative staff (who can serve permanently) and members of interest groups (lobbyists) would have much more power because of their greater familiarity with issues and procedures.