If you are named as executor in your sister's will, and if it is proper to probate her will in Texas, then you can hire a Texas attorney to probate the will for you. You can probably hire an attorney over the telephone.
Some Texas courts may allow you to appear by deposition, but the customary practice is for the applicant to attend a hearing several weeks after the application for probate is filed. At the hearing, the applicant gives a few minutes of testimony, and is then usually appointed as executor. From there, the executor can often fulfill his/her duties through the assistance of the Texas attorney.
A referral from a lawyer you know and trust, to a lawyer that knows this practice area, is best. Be careful of referrals from non-lawyer friends and relatives. Consider using the search function on Avvo or on lawyers.com to find a lawyer. Look for an Avvo Rating of "10", a lawyers.com Peer Review Rating of "AV Preeminent, 5.0", and/or board certification.
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Hire an attorney in the county where your sister lived. Discuss (many will Skype or talk in the phone) with your lawyer whether you need to appear in person. It will depend in part on what court it is in.
This answer DOES NOT establish an attorney-client relationship. This answer is based on the limited information provided and is not intended to be conclusive advice. There are likely other factors that might influence or change the advice after a more lengthy consultation.
I agree with the other attorneys. Most counties in Texas will allow you to move through the process without a personal appearance. Many of us who handle probates in Texa have handled such situations. If your sister was in another state, you may want to re-ask this question listing her location to alert attorneys in that area to answer your question.
Kendall Cockrell is an attorney with The Cockrell Law Firm in Beaumont, Texas. None of the opinions he states on this site constitute an attorney-client relationship. For more information, contact The Cockrell Law Firm. Contact information available on Kendall Cockrell's profile on this site.