DPB Online has now updated this page.
Viscount Howick, Alexander Edward GREY (b. 1968), has succeeded his father in his peerages, and is now the 8th Earl. He is married with a daughter.
The line of succession begins with descendants of the Hon George GREY (1809-1891), 5th son of the 2nd Earl. At the head of the line, as colinp had posted, is CHRISTOPHER JOHN (B. 1946), followed by his son, Duncan Colin (b. 1974).
The rest of the "immediate" line is as follows:
3. David York (b.. 1947), brother of CHRISTOPHER
4. Michael Colin (b. 1982), son of David.
5. Charles David (b. 2017), son of Michael and grandson of David.
6. Simon Alexander (b. 1958), half brother of CHRISTOPHER and David.
7. Marcus Edward (b. 1960), brother of SImon and half brother of CHRISTOPHER and David.
Next in line are the descendants of the 3rd son of the 1st Earl, the Hon George GREY (1767-1828), created a baronet (UK) 1814):
8. Sir Anthony Dysart GREY, 7th Bt. (b. 1949)
7. Thomas Jasper, son of Sir Anthony and ha to the baronetcy (b. 1998)
There are other descendants after them, from the Rt. Rev. Edward GREY, Bishop of Hereford (1782-1937), 5th son of the 1st Earl.
Brooke