having the tenant release their claim would be the easiest but if that doesn't happen, you might have legal rights to terminate the tenancy.
1. you need to refer to the deed but some life estates (and I stress some) are written that the estate is only for as long as the tenant resides in the premises.
2. if the tenant does not pay the costs required as a tenant, you could seek to have the tenancy terminated.
and while not as marketable, you can actually sell your interest (presuming you are a remainderman). Obviously the buyer could not take possession until such time the life estate is terminated for whatever reason. This does reduce the value of the interest in the house at the current time.