Extended locally in(out)-semicomplete digraph is an important generation of semicomplete digraph.The degree-constrained conditions for an extended locally in-semicomplete digraph to be traceable are obtained by applying the multi-insertion approach.A sufficient condition for the extended locally out-semicomplete digraph to be traceable is also derived from the property that an extended locally out-semicomplete digraph is the converse of the corresponding extended locally in-semicomplete digraph.