Upgrade new bike to 11 speed or downgrade trainers wheel to 8 speed
The spacing/pitch between the individual cogs of the 8 and 11 speed cassettes are different so if you want to make the training bike work properly with the 11spd cassette you will have to replace your right side shifter (shifter for the rear derailleur) with an 11 speed version or with a friction shifter. Also since (as pointed out by @Argenti Apparatus) the actuation ratio of 8 and 11 speed derailleurs are different, you will need to replace the derailleur with an 11 speed compatible derailleur. Removing a few cogs from the 11 spd cassette won't work due to the different cog spacing as long as you don't upgrade to an 11 SPD shifter due to the different spacing between the cogs. You can ride it but you won't be able to properly index it and the drivetrain will wear out faster and you probably won't be able to shift into some of the gears due to not being able to properly index it.

Do keep in mind 8 speed cassettes are a lot cheaper than 11 speed so the replacement parts (cogs or entire cassette, when the current cassette is worn) will be more expensive also.