One of the artefacts that have been excavated from the recently discovered archaeological site are estimated at being more than 2000 years old.
(A) have been excavated from the recently discovered archaeological site are estimated at being
Subject-verb agreement error - singular subject, plural verb - in the main clause the subject is singular "one" thus we need the singular "is"
(B) have been excavated from the recently discovered archaeological site are estimated to be
Subject-verb agreement error - singular subject, plural verb - in the main clause the subject is singular "one" thus we need the singular "is"
(C) has been excavated from the recently discovered archaeological site is estimated at
Subject-verb agreement error - plural subject, singular verb - "that" refers to "artefacts" thus we need the plural "have" in the essential modifier
(D) have been excavated from the recently discovered archaeological site is estimated to be
"that" refers to "artefacts" thus we need the plural "have" in the essential modifier and in the main clause the subject is singular "one" thus we need the singular "is". And the correct idiom is "estimated to be"
(E) has been excavated from the recently discovered archaeological site is estimated to be
Subject-verb agreement error - plural subject, singular verb