Navies around the world do a variety of things from HDAR or Humanitarian Aid Disaster Response/Relief to fighting wars and hunting submarines, and various exercises, but other operations include Anti Piracy, Blockades and Anti Terrorism Patrols.
Here are some of the various Operations the Royal New Zealand Navy have taken part in recent times.
Operation Active Endeavour
Operation Active Endeavour was a maritime operation of the North Atlantic Treaty Organization. It operated in the Mediterranean Sea and was designed to prevent the movement of terrorists or weapons of mass destruction. It had collateral benefits in enhanced security of shipping in general. It was one of the first military actions taken by NATO in response to an invocation of Article 5 of the North Atlantic Treaty which provides for collective defense and the first ever operation conducted by the Alliance in direct application of the defence clause of the Treaty. In November 2016 it was replaced by the non-Article-5 Operation Sea Guardian.
HMNZS Te Kaha (F77) took part.
https://en.wikipedia.org/wiki/Operation_Active_Endeavour
Operation Enduring Freedom
Operation Enduring Freedom (OEF) was the official name used by the U.S. government for the Global War on Terrorism. On 7 October 2001, in response to the September 11 attacks, President George W. Bush announced that airstrikes targeting Al Qaeda and the Taliban had begun in Afghanistan. Operation Enduring Freedom primarily refers to the War in Afghanistan, but it is also affiliated with counterterrorism operations in other countries, such as OEF-Philippines and OEF-Trans Sahara. After 13 years, on 28 December 2014, President Barack Obama announced the end of Operation Enduring Freedom in Afghanistan. Continued operations in Afghanistan by the United States' military forces, both non-combat and combat, now occur under the name Operation Freedom's Sentinel.
Combined Task Force 150 (CTF-150) HMNZS Te Kaha (F77) & Te Mana (F111) took part
https://en.wikipedia.org/wiki/Operation_Enduring_Freedom
Combined Task Force 150
Combined Task Force 150 (CTF-150) is a multinational coalition naval task force working under the 33-nation coalition of Combined Maritime Forces and is based in Bahrain established to monitor, board, inspect, and stop suspect shipping to pursue the "Global War on Terrorism" and in the Horn of Africa region (HOA) includes operations in the North Arabia Sea to support operations in the Indian Ocean. These activities are referred to as Maritime Security Operations (MSO).
Countries presently contributing to CTF-150 include Australia, Canada, Denmark, France, Pakistan, Japan, Germany, the United Kingdom and the United States. Other nations who have participated include Italy, India, Malaysia, Netherlands, New Zealand, Portugal, Singapore, Spain, Thailand and Turkey. The command of the task force rotates among the different participating navies, with commands usually lasting between four and six months. The task force usually comprises 14 or 15 ships. CTF-150 is coordinated by the Combined Maritime Forces (CMF), a 33-nation coalition operating from the US Navy base in Manama, Bahrain.
Combined Task Force 150 (CTF-150) HMNZS Te Kaha (F77) & Te Mana (F111) took part
https://en.wikipedia.org/wiki/Combined_Task_Force_150
Operation Ocean Shield
Operation Ocean Shield was NATO's contribution to Operation Enduring Freedom – Horn of Africa (OEF-HOA), an anti-piracy initiative in the Indian Ocean, Guardafui Channel, Gulf of Aden and Arabian Sea. It follows the earlier Operation Allied Protector. Naval operations began on 17 August 2009 after being approved by the North Atlantic Council, the program was terminated on 15 December 2016 by NATO. Operation Ocean Shield focused on protecting the ships of Operation Allied Provider, which transported relief supplies as part of the World Food Programme's mission in the region. The initiative also helped strengthen the navies and coast guards of regional states to assist in countering pirate attacks. Additionally, China and South Korea sent warships to participate in these activities.
The US Navy was the largest contributor of ships, followed by the Indian Navy. The taskforce was composed of ships from the contributing navies, led by a designated leadship. The role of leadship was rotated among the various countries involved. In October 2015 this was the Turkish frigate TCG Gediz.
HMNZS Te Mana (F111) took part
https://en.wikipedia.org/wiki/Operation_Ocean_Shield
International Force East Timor
The International Force East Timor (INTERFET) was a multinational non-United Nations peacemaking taskforce, organised and led by Australia in accordance with United Nations resolutions to address the humanitarian and security crisis that took place in East Timor from 1999–2000 until the arrival of UN peacekeepers. INTERFET was commanded by an Australian military officer, Major General Peter Cosgrove.
HMNZS Te Kaha (F77) Canterbury (F421) and the replenishment ship HMNZS Endeavour (A11) took part
https://en.wikipedia.org/wiki/International_Force_East_Timor
