Constructing a pushdown automaton that accepts L*
The Kleene star is, as you know, the union $\bigcup_n L^n$ of arbitrary powers $L\cdot L\cdot\ldots\cdot L$ of $L$.

If $M$ is the automaton that accepts $L$, then in order to make an automaton for $L^*$ you basically have to make it possible to restart the automaton after accepting $L$. Be careful in choosing final state or empty stack acceptance.