Assume we have an algorithm HC for HAMILTONIAN CIRCUIT. How is it possible to convert the HC algorithm to an algorithm HP for HAMILTONIAN PATH?
The wording of the question is a bit unclear. You're supposed to reduce HamiltonianPath to HamiltonianCircuit: in other words, write an algorithm that solves HamiltonianPath by using a subroutine for HamiltonianCircuit.

I assume you're specifically going for a polytime reduction, so you shouldn't do an exponential amount of work in your new program—but there are a few different types of polytime reductions (Karp vs Cook in particular), and I can't get any more specific without knowing which one you're using. In a Karp reduction, for example, you only get to call the HamiltonianCircuit subroutine once, and have to return its output unmodified—all the transformation has to happen before you make the subroutine call. In a Cook reduction you can call it as many times as you want, and transform the outputs however you like before returning.