Shakedown cruise

A shakedown cruise tests a new starship's systems. Most starships undergo a shakedown cruise to determine any faults or problems with the ship's systems, as well as determining performance issues.

The USS Excelsior was undergoing a shakedown cruise with its experimental transwarp drive when Starfleet ordered it to intercept the stolen USS Enterprise from Spacedock. Unbeknownst to her crew, Montgomery Scott had sabotaged the Excelsior to allow the Enterprise to escape. 

Former Enterprise senior officers Captain James T. Kirk, Montgomery Scott and Pavel Chekov, as well as journalists from various news outlets, were aboard for the USS Enterprise-B's shakedown cruise in 2293 when it turned into a rescue mission. Kirk was assumed killed when the Nexus slammed into the Enterprise-B's deflector control room. 

In 2371, on Stardate 48650.6, the USS Prospect-A responded to a distress call during its shakedown cruise. Damage to the ship during the scuffle was light, but Captain John Sill expressed he'd hoped those at the commissioning ceremony hadn't roughed up his new ship too much. (Star Trek: The Prospect Chronicles)

By 2373, the USS Enterprise-E was nearing completion of its year-long shakedown cruise when it responded to a Borg attack on Earth.