The phrase "a second shipment of" is correct and usable in written English.
You can use it when referring to an additional delivery or consignment of goods that follows a previous one.
Example: "We are expecting a second shipment of supplies to arrive by the end of the week."
Alternatives: "another delivery of" or "a follow-up shipment of".
Meanwhile, a second shipment of Benefit's Big Beautiful Eyes contour kit arrived in stores this month.
Last October he sent a second shipment of 28 wild dolphins to Dubai.
Meanwhile at Barneys New York on Madison Avenue, a second shipment of Wolford fishnets have completely sold out.
A second shipment of 654,000 ballots was scheduled to begin a similar journey from Miami-Dade County on Friday morning.
A second shipment of teddy bears, from the Dade County school board in Florida, was directed to District 27 in Queens and District 31 in Staten Island, neighborhoods that were home to many firefighters and thus had a disproportionate number of students who lost parents.
A second shipment of emergency supplies will arrive early next week, and will be distributed at NRG Center in Houston, as well as Austin and San Antonio Communities.
In 2008, Mr. Brust made a first shipment of 90,000 liters, or 24,000 gallons, of beer to China.
Before the broadcast, Al-Manar sent out text messages that paraphrased Mr. Assad as saying Syria had already received a first shipment of the S-300 missiles.
The Friendship Bridge between Uzbekistan and Afghanistan, closed for years by enmity and fear, opened today and a first shipment of aid came across.
Finally, this week, it was reported that a first shipment of 500-bolivar notes has been ordered and will be distributed through banks in the coming weeks.
The so-called Friendship Bridge between Uzbekistan and Afghanistan opened yesterday, and a first shipment of grain and medicine was sent across by train, heading for the refugee camps.
