The phrase "a second consignment of" is correct and usable in written English.
It can be used when referring to the delivery or shipment of goods, indicating that this is the second batch being sent.
Example: "We have just received a second consignment of the new product line, and it is ready for distribution."
Alternatives: "a second shipment of" or "a second delivery of".
But a July 2000 attempt to smuggle a second consignment of arms was foiled by Croatian police, who seized seven RPG-18s, AK-47 assault rifles, detonators, ammunition, and twenty packs of TM500.
A second consignment of 45,000 Oral Rehydration Salts, 34,000 jerrycans, 900,000 water purification tablets and 900 kilos of chlorine powder is being dispatched this week.
A first consignment of turkeys arrived at the Bernard Matthews plant in Holton, Suffolk, yesterday after the government gave it the go-ahead to restart operations.
A first consignment of medical supplies which arrived on Friday is currently being distributed in various parts of the country.
The Hales sent the first consignment of aoogs and now are ready to send a second consignment.
This second consignment of goods follows seven truck-loads of supplies sent by UNICEF to assist the one million people affected by the massive flooding.
India will be importing its first consignment of U.S. liquefied natural gas, a mere six months on from marking its first consignment of American crude oil.
During incident I the health protection team had only a few hours advanced notice before delivery of the first consignment of poultry carcasses to the plant.
Its official – India will be importing its first ever consignment of U.S. liquefied natural gas (LNG), a mere nine months on from signing up for its first consignment of American crude oil.
His first consignment of vines was labelled "scyras" which many thought was a misspelling of Syrah.
The first consignment of Syrian chemical weapons materials left the country on a Danish ship on Tuesday.
