When does the time limit start in Non Compete agreement?

It would depend on the term of the agreement. Did it terminate upon your termination of employment? If so, it would not be in effect when you were reemployed, so you would have needed to sign a new agreement.

The answer to your question depends entirely upon the exact verbiage of the agreement that you signed. All other things being equal, I would doubt that the period of re-employment would re-start the three year period. In that regard, it is noteworthy that three years is a rather long time period for a non-compete. Most such agreements provide a period of one or two years. Non-compete agreements are evaluated as to whether the duration and the geographic area are reasonable. You should bring the agreement to a local attorney for review. Good luck to you.

You need advice from an attorney licensed in Texas. Texas has a law dubbed the Covenants Not to Compete Act which limits the enforceability of such agreements. This varies from the general concepts taught in law schools in the U.S. To be enforceable in Texas, a non-compete agreement with an employee must be ancillary to or part of an otherwise enforceable agreement (the "consideration requirement"), and the employment agreement alone doesn't count unless the agreement states that the employer is providing additional consideration to the employee, for example, a bonus, or even the promise to provide confidential or proprietary information to the employee. If it has the consideration requirement, the agreement must also be reasonable in scope / territory / time such as (i) restrain no more professional activity than is necessary to protect the legitimate interest of the employer (can't restrain what the employer doesn't do); and (ii) restraint in territory of the legitimate business of the employer, but the entire U.S. is not necessarily okay. Note that if (i) or (ii) are ridiculous, the 3-year requirement is about as long as one could go. However, if the agreement is unreasonable, a Texas court is permitted to re-draft the contract to make it reasonable so you're not out of the woods. Take a look at the agreement and see if you received anything in exchange for the non-compete covenant. The fact that the agreement was signed more than 3 years ago is a red flag in that the Covenants Not to Compete Act wasn't enacted until September 2009, not to mention that you would also need to receive new consideration for the re-hire separate from the first date of hire, another red flag. Even if the agreement is arguably unenforceable, non-compete agreements can be a tricky situation in that I've seen companies assert these provisions in instances where they don't precisely apply because employees leave under less-than-desired conditions, so keeping things above board with the company departed before and after you leave is always prudent. If you're taking a job with a new employer, consider discussing the agreement with a new employer, but not during the first interview. A discussion that you'd have where you tell them that you're subject to such provision and that you're planning on hiring an attorney to assist you. The company may also want you to clarify the obligations so they can measure their own risks. Best of luck to you. You should not consider this as counsel or legal advice until we have reviewed and discussed your agreement thoroughly. Consult an attorney with the specifics of your circumstances and for the review of your agreement so that an appropriate determination can be made.