If you just cut down the unwanted plants and left the roots in situ, they will continue to try to grow all the time. The only way to stop that is to treat the stumps with stumpkiller, something like SBK brushwood killer (http://www.vitax.co.uk/home-garden/sbk-brushwood-killer/, by drilling into them and applying the product to the wells or holes you've made. If there aren't any visible stumps, you'll need to dig around and treat major roots in a similar way instead, obviously being careful that you don't treat the roots of the tree you want to keep by mistake. If you can't find SBK, there should be similar treatments available where you are, but if you do use SBK, although it tells you to dilute it, I never do for killing tree stumps, I simply apply the product neat, and very, very carefully, to the holes I've drilled, and cover afterwards. It's important not to spill it anywhere else, including the soil.
The other option is to remove all stumps and roots to a depth of a foot to 18 inches.