In general, a contract must ongoing in order to be varied and can only be varied as provided for in its terms or if consideration is made by both parties for the variation.
If the non-complete contract has a provision in it that allows its term to be varied (unilaterally or by agreement) then the revised term would be binding if done in accordance with it.
If not, then unless you were given consideration for agreeing to an extension (or gave consideration for agreeing to a reduction) then the variation would be unenforceable. Consideration cannot be an existing obligation (so them letting you keep your job is not consideration) but it could be something tied up with the employment contract (for example, if the change occurred in conjunction with a pay rise then (part) of that pay rise could be consideration for the variation).
You can vary a contract without consideration if the variation is executed as a deed.