Dust on the sea is a classical sequel. It starts about two weeks after "RSRD" (I just love the american acronym fetish) ends.
There's differences in the narrative technique as RSRD is first person while DOTS
is "kind of" third person, but with Richardson being the narrator 90% of the time anyway.
Personally I liked dust on the sea better, since there, most of the action is concentrated on a single war patrol, while RSRD spans a time from just before Pearl Harbor to late 1944.
Also, DOTS is written in the 1970s, where Beach could reveal a lot which was still classified by the time he wrote the first, like Ultra or details about approach technique or radar and radio performance.
I ordered his third "cold is the sea" as well, but since it is being delivered from the US, I suppose it will take some time.
In that one, a much older Richardson takes command of one of the first SSBNs in the 1960s.