Clark - the former head of the UN Development Programme - said it was disturbing that nothing had been done to implement the council's resolution calling for a complete ceasefire in the occupied Palestinian territory of Gaza.
"The Security Council has a responsibility to chart a path towards a sustainable peace. A full, immediate, and complete ceasefire in Gaza is an indispensable step," she said in a speech to the council in New York early on Friday morning (New Zealand time).
"It is deeply disturbing that Security Council Resolution 2735 calling for this remains unimplemented."
The approach to the conflict pursued by powerful members of the international community had "failed", and a new approach was needed, grounded in international law, she said.
"Council members who question the binding status of these resolutions, or who use their veto to protect an ally or to oppose a geo-political rival, are eroding the Council's authority. They also undermine their own reputations and long-term interests."
Clark also said Palestine should be recognised as a state and given full UN membership.
She called on UN member states to respect and comply with the International Court of Justice's recent advisory opinion that concluded that Israel's presence in the occupied Palestinian territory was unlawful and must end as rapidly as possible.
While that opinion was non-binding, it was an "authoritative, landmark ruling", she said.
"The General Assembly and Security Council should give effect to the Advisory Opinion by passing resolutions endorsing it and setting out what action is required by Israel, other Member States, and the UN to bring an end to the occupation."
Settlements continued to expand in the West Bank and East Jerusalem while international attention was focused on Gaza, she said.
"More decisive Member State action is needed."
Clark also called on UN member states to refrain from giving assistance to, or trading with, any illegal settlements.