The £170,000 position became vacant after Tony McArdle stepped down following more than 12 years in the role.
The chief executive will be expected to deliver services to maintain community safety, promote business growth, and improve health and wellbeing among the 750,000 residents it serves in the county.
They will have to deal with reduced central government funding, which has placed a strain on councils across the country, and address key local issues post-Brexit.
In promoting the post and Lincolnshire as a place to live, county council leader Martin Hill said: “Our new chief executive will be expected to drive our vision forward, inspiring a skilled and dedicated 4,500-strong workforce at the sharp end of local government change.
“They’ll also need to display commercial acumen and a capacity for innovation as we continue to adapt to falling budgets without letting standards slip. It won’t be easy – but nothing worth doing ever is.
“From a Lincolnshire family myself, I am passionate about the county – its history, farming and food, manufacturing excellence, RAF connections and more.
“Above all, I am determined to deliver for its people – and I want a chief executive alongside me who feels the same.”
The closing date is noon on Monday, March 26, so applicants have just under two weeks to send in their CVs.
A longlist will be drawn up by Tuesday, April 3, with technical interviews taking place the following week.
The interviews will also give candidates the chance to meet the council leader.
An assessment centre will be held on Wednesday, April 18 and Thursday, April 19.
Councillor Hill said that the council hopes to appoint the new chief executive at a meeting of the Full Council on May 11, before he or she takes over fully in July.
Executive Director for Environment and Economy Richard Wills is currently acting as head of paid service and returning officer for county council by-elections.