apple tree with no fruit

I INHERITED A SITE/GARDEN WITH SOME APPLE TREES UPON IT ,I AM TOLD THAT THEY PROBABLY GREW FROM SEEDS THAT WeRE THROWN OUT ABOUT 40 YEARS AGO . LAST YEAR I PLANTED 2 NEW APPLE TREES ALONGSIDE THE OLD ONES. THERE WAS PLENTY OF FRUIT LAST SEPT/OCT BUT THIS YEAR I HAVE NONE. SHOULD I REMOVE THE OLD TREES AND PLANT ALL NEW YOUNG TREES?