Do I need to obtain a permit for moving electrical and plumbing work if I am located outside of city limits in Texas?

Edit to add Fort Bend County.

Texas does have Residential Building CODE restrictions
Your licensed plumber & electrician will know where/to whom permit applications need to go for approval.
If DIY is on your mind, then probably resale w/creditials is not and pretty rural but since a chance such a gamble might pay off in the long run.
In some cases in Texas, this is the County (so phone them) or only the Power Co, Water Co, if any etc.

Hope you get a better, specific to Fort Bend answer soon.

Unincorporated areas normally do not need a permit for repair/alterations to single family dwellings. Looking over their website would seem to concur.

If your plumbing work involves septic modifications, then that will trigger some review as that is regulated at the County level for obvious reasons. Otherwise, I would say no permit required.

Just give them a call!

All of Texas is covered by the IRC 2015 and local municipalities can adopt new versions of the IRC. For instance Austin recently adopted (with amendments) the 2021 IRC.

Now the issue is not which code was adopted, but who will inspect it. Cities, like Austin, Smithville, Bastrop - all have permit and inspection departments. Unincorporated areas (County) do not. So therefore - no Building Permit application/inspection is required.

We are talking residential not commercial - that is a different ballgame as counties do require commercial building permit and inspection in unincorporated areas.

HTH

Only if your county requires it. A homeowner in Texas can legally do all of their own home repairs. Some utilities might require a paid inspection.

Best part about living in the country. You can do whatever the hell you want. Personally, I try to stick to all standard codes though. All modifications with electrical panels or construction I did on my last house were not permitted and the new buyers had no clue they were ever done. It passed inspection so....again...best to follow codes and read up on them.