Delete elements of list with certain length

Select[a, Length@# != 1 &]

{{0, 5, 2, 15, 6, 9, 3}, {5, 5, 5}, {4, 4, 5, 6}}

Also

GeneralUtilities`Discard[a, Length[#] == 1 &]

{{0, 5, 2, 15, 6, 9, 3}, {5, 5, 5}, {4, 4, 5, 6}}

and

DeleteCases[a, _?(Length@# == 1 &)]

{{0, 5, 2, 15, 6, 9, 3}, {5, 5, 5}, {4, 4, 5, 6}}

This might be faster than klgr's solutions on large lists:

Pick[a, Unitize[Length /@ a - 1], 1]

Select and DeleteCases are known to be kind of slow.