Kear, the 62-year-old former Sheffield Eagles, Huddersfield Giants and Hull boss, rejoined Trinity – where he was coach from 2006-2011 – in the off-season after five years at Batley Bulldogs.
He told the club’s website: “I am really pleased.
“I have got great affection for the club as most people will know from my first stint here. I have enjoyed working with Michael [Carter, Wakefield’s chairman] Chris [Chester, head coach] and the coaching staff this season, so I am really looking forward to next year.
“It is great to see how much we have improved on last season, but we still have plenty to do over the next six weeks.”
Carter said: “I am delighted that John has agreed to commit for another season. His passion for this club and rugby league in general is there for all to see and he brings an experience to both myself and Chris that money cannot buy.
“The club is moving in the right direction and John is a big part of that.”
Second-rower Crowther, 20, has signed a one-year extension to his deal.
The Trinity Academy product said: “I am really happy, I have been with Wakefield since I was 15 so it is really nice to be able to stay, especially when it is your home town club as well.
“I haven’t played as many games as I would have liked to this season, but the competition is strong. Hopefully next year I can kick on in pre-season and get a few more games.”
Chester added: “I am delighted for Jordan to have signed a new deal with us and it is fantastic to be able to secure players who are products of our academy.
“Jordan is still only young, but I have seen a lot of potential in him that will see him go a long way and I look forward to working with him for the remainder of this season and the next.”