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Yes, that is how I read that agreement. Where we typically see this sort of language, it involves an employment agreement and the language is intended to be effective during the entire employment and for one year after the employment ends.
So, it would read like this: "Employee will not, either during employment with Employer or for a period of two years thereafter, directly or indirectly, for himself/herself or any third party, accept employment or engage in any business or activity which is directly or indirectly in competition with Employer."
For the agreement to make that year start at some other point than the date the agreement was entered into, it has to have that sort of language. I don't see that language there. What I see is an agreement with a non-compete the ends on the "effective date" which should be a dated defined in the agreement, or it is the date that both parties completed execution of the agreement.