Oslo-listed Avance says the 83,000-cbm Monsoon (built 2015) has been fixed on a 60 to 90 day voyage at a rate reflecting the contemporary market.
It is suggested a figure of around $55,000 daily has been secured.
A sistership, the Mistral, is under final negotiations for similar employment, Avance told investors on Friday.
Christian Andersen-led Avance says the next two ships in the series, hulls 1073 and 1074 ,will be delivered in the first and second quarters respectively.