keeping a secret or furtive watch
"The security guard caught the intruder spying through the keyhole before he could slip into the office."
the act of keeping a secret watch for intelligence purposes
"The security team caught the intruder spying on our confidential documents from across the fence."
espionage
"The novelist spent years researching her latest book by interviewing former CIA officers who shared their experiences of spying during the Cold War."
present participle of spy
"The detective spent hours spying on the suspect's house to gather evidence for the trial."