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 -> "estimated at being" is incorrect. Another issue, we have subject, one (singular subject).....are (plural verb)...Incorrect.
(B) have been excavated from the recently discovered archaeological site are estimated to be -> we have subject, one (singular subject).....are (plural verb)...Incorrect.
(C) has been excavated from the recently discovered archaeological site is estimated at -> One of "artefacts" (plural), so need "have been"....Incorrect to use "has been".
(D) have been excavated from the recently discovered archaeological site is estimated to be -> Both subject verb agreement issue is resolved. Let's keep it.
(E) has been excavated from the recently discovered archaeological site is estimated to be -> One of "artefacts" (plural), so need "have been"....Incorrect to use "has been".
So, I think D.