A clandestine operation is an operation or action funded, organised and run with the specific aim of ensuring secrecy and lack of detection. As well as being the stock-in-trade of intelligence gathering and espionage missions, the term can also refer to military/paramilitary operations.
This differs from a covert operation in that the accent is on concealing the instigation, conduction and effects of the operation itself. In a covert operation, it is the identity of the sponsor that is obscured, often because the consequences of the op are too obvious to conceal. To illustrate, the sharp end of the Central Intelligence Agency is known as the Clandestine Service - its objective is to gather intelligence without anyone outside the agency having any knowledge.
Clandestine ops is a murky area to research. A good fictional example would be the SHOWBOAT operation in the novel Clear and Present Danger. In the story, the CIA infiltrated soldiers into Colombia to report on the departure of US-bound drugs shipments. This operation was clandestine rather than covert because the targets were not aware of its existence. Once the soldiers' orders changed to active interdiction and combat, the effects became obvious to the smugglers. As the identity of the perpetrators was deliberately hidden, this technically became a covert operation.
An example in the real world is the 1947 Operation Gladio. This established CIA cells in Italy, along with sister operations Glaive in France; Schwert in Austria; Sheepskin in Greece; Sveaborg in Sweden and P26 in Switzerland. The objective of these cells was to "stay behind" after a Soviet invasion, sabotaging pre-selected transport, industrial and military sites. Clandestine as it was, neither the Soviets nor the host countries were aware of such CIA groups.
The Century Foundation, a left-of-centre think tank on governmental and social affairs, researched American clandestine operations after the 1994 arrest of Aldrich Ames. Its recommendations were that clandestine paramilitary action by the CIA or other government entities should be pared back, with remaining capability focussed on immediate threats to US interests.
Central Intelligence Agency, Specialoperations.com. http://www.specialoperations.com/Domestic/CIA/default.html
Clandestine Service, Central Intelligence Agency. www.cia.gov/employment/clandestine.html
The Fourth Force, Col. L Fletcher Prouty Reference Site. http://www.prouty.org/4thforce.html
David Guyatt, Operation Gladio. http://www.copi.com/articles/guyatt/gladio.html
Improving and Streamlining the Clandestine Service, The Century Foundation. http://www.tcf.org/task_forces/future_of_intelligence/Recommend3.html
Tom Clancy, Clear and Present Danger, Fontana 1990.