Ashurst is sidelined by a knee problem while Gigot hyper-extended his elbow in Trinity's 48-18 win over the Robins last weekend.
Gigot scored in the match, in what was Trinity's second-straight victory while Ashurst had claimed a try on Thursday night as Wakefield defeated Huddersfield Giants.
"We have lost Matty Ashuurst, he has gone for the year," confirmed head coach Chester, who is preparing his side for a clash with Leeds Rhinos tomorrow afternoon.
"Tony Gigot has hyper extended his elbow and that certainly rules him out as well.
"It is disappointing for both of those guys, especially Tony because he has been stood down a couple of times through track and trace.
"He has not been able to get a run of games. Looking back, it is probably because he has not had a full pre-season under his belt.
"I am disappointed for those two guys but it means some young kids can get a chance next week."
Leeds could be forced to stand some players down for the fixture after their opponents from Monday night, Castleford Tigers, reported 12 cases of Covid-19 on Wednesday morning.
Wakefield have returned all negative tests although will be without Jay Pitts, Craig Kopczak and Titus Gwaze who are self isolating.
Chester added: "We are all negative, which is another real bonus.
"We have still got a few guys, Pitts, Kopczak and Gwaze, who are still at home and one member of staff but they should be in and around the squad over the next few days.
"We are not to sure about the Salford game next week. Things are looking good.
"These guys have gone through the mill these last 14 weeks. Just looking at the squads and teams we have put out, there is not one week we have been able to go with the same 13 for one reason or another.
"It is nice to have that continuity and that breeds confidence and the players are playing with confidence now.
"It is another step up against Leeds on Thursday night, we are not going to get the cheap possession we got against Hull KR at the weekend.
"But it is amazing what a couple of wins does."
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