...and reading below it appears that Teversal FC will be playing in the NCEL in the 2016/17 season.
However, The FA have the last word and many non-league forecasters have Teversal FC set down for a lateral move into the East Midlands Counties League.
We will wait and see.

The NCEL article says...

The FA Leagues Committee have today approved the allocation of clubs in the Toolstation NCEL Premier Division and Division One for the 2016/17 season.

There will be 22 clubs in both divisions with Harrogate Railway Athletic coming down into the Premier Division from the Northern Premier League whilst AFC Mansfield, Bottesford Town and Hemsworth Miners Welfare come up from Division One.

Coming into the league in Division One will be Campion from the West Riding County Amateur League and either Ollerton Town or Harworth Colliery Institute from the Central Midlands League and the three teams relegated from the Premier Division are Brigg Town, Nostell Miners Welfare and Pontefract Collieries.

Leaving the league are Tadcaster Albion who are promoted to the Northern Premier League whilst Lincoln Moorlands Railway and Hull United depart from Division One.

TOOLSTATION NCEL PREMIER DIVISION

1. AFC Mansfield (from Div 1)
2. Albion Sports
3. Armthorpe Welfare
4. Athersley Recreation
5. Barton Town Old Boys
6. Bottesford Town (from Div 1)
7. Bridlington Town
8. Cleethorpes Town
9. Clipstone FC
10. Garforth Town
11. Handsworth Parramore
12. Harrogate Railway Athletic (from Northern Premier League)
13. Hemsworth Miners Welfare (from Div 1)
14. Liversedge FC
15. Maltby Main
16. Parkgate FC
17. Pickering Town
18. Rainworth Miners Welfare
19. Retford United
20. Staveley Miners Welfare
21. Thackley FC
22. Worksop Town

TOOLSTATION NCEL DIVISION ONE

1. AFC Emley
2. Brigg Town (from Prem Div)
3. Campion FC (from West Riding County Amateur League)
4. Dronfield Town
5. Eccleshill United
6. Glasshoughton Welfare
7. Grimsby Borough
8. Hall Road Rangers
9. Hallam FC
10. Knaresborough Town
11. Nostell Miners Welfare (from Prem Div)
12. Ollerton Town/Harworth Colliery Institute (from Central Midlands League)
13. Penistone Church
14. Pontefract Collieries (from Prem Div)
15. Rossington Main
16. Selby Town
17. Shirebrook Town
18. Teversal FC
19. Westella VIP
20. Winterton Rangers
21. Worsbrough Bridge Athletic
22. Yorkshire Amateur

The allocation will be ratified at the NCEL's Annual General Meeting which takes place in Scarborough on Saturday 18th June, 2016.