colinp, I haven't been able to find anything to say Sir Charles actually died.
If he did, he is succeeded by his only son, Charles Lawrence Somerset (b. 1990) a 2012 Olympian. (He represented Great Britain in the 110 Meter Hurdles in track and field).
According to Debrett's latest edition, he is unmarried so the heir presumptive would be Nicholas Orme Clarke (b. 1976), a grandson of the 5th Bt.
Nicholas is married with a son and a daughter. His son, Julian Nicholas William (b. 2014), would be next in line.
Hope this helps.
Brooke