This depends on what specifically you are referring to when you say "is up."
When the level term period is over, the premium will generally increase. If the policy owner wishes to pay the premiums and keep the policy, he or she has that option.
Term policies will reach a point where they can no longer be continued. In this circumstance, the policy terminates and coverage is no longer available from the policy.
When the term is up on a term life insurance policy, either the policy ends, or the policy goes into an annually renewable term (unless it has a rider or feature that enables it to enter a new level premium at a higher price). This new annually renewable premium is much higher than the original term premium was and can go up every year after that.
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When the level term period is over, the premium will generally increase. If the policy owner wishes to pay the premiums and keep the policy, he or she has that option.
Term policies will reach a point where they can no longer be continued. In this circumstance, the policy terminates and coverage is no longer available from the policy.