He is running in a "New District" and the only other person running for the position doesn't have a chance of winning...
I assume you're talking about the new House District 106 and Tan Parker (incumbent representative of current House District 63). Is an incumbent representative who has to change districts due to redistricting considered a "freshman" if they win reelection? I happen to know Rodney Caston, the LP candidate, personally. I expect Parker will win.
While it's great that Parker voted against Joe Straus for Speaker, I have no reason to suppose that his motivations included 2A issues. I can't find any occurrence of the words "gun" or "firearm", or any discussion of the 2nd amendment or gun rights, on his official website. Really, all his site talks about is anti-immigration policies and lower taxes (primarily for special interest groups). He talks an awful lot about states rights, but I can't find a single clear assertion of individual rights. While I'll acknowledge that his official website may just not convey his principles very well, from the information I have available, he seems like little more than Yet Another Republican. If that's the case, don't expect any more than lip service paid in support of improving protection of gun rights in Texas from him. A lot of Republican Representatives said they'd support open carry legislation in 2011. A number not too different from zero actually did.
When he does more than issue a yes-or-it-looks-bad vote on a motion to report an open carry bill out of committee, I'll think about considering him to be pro-2A. Actually, do we have any documented proof that he did, in fact, vote yes on that? It seems obvious that, since he's on that committee, he would have voted yes, but the vote was 5-3, and I can't find record of the individual votes.
P.S. I'm aware that HB 2756 never made it to general debate. I'm also aware of what was considered higher priority (yes, I know Joe Straus controls the schedule). My conclusion is that Republican priorities are jacked to hell, and I don't expect them, as a group, to give two turds about individual liberty, since it doesn't make for tasty campaign donations.
P.P.S. I'm further aware that, three sessions ago, Tan Parker voted in favor of the use of deadly force in self defense. Also an "of course" vote, in my book.