Harris will be able to serve two terms. The 22nd amendment says:
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once
The second clause applies to vice presidents taking over, but since there’s less than two years left in Biden’s term, it won’t come into effect.