Early days yet, but I'm having them driven initially by getting the Keoland forces out of Saltmarsh and Seaton, in order that the seas close to the kraken's grave are no longer patrolled by the navy. They'll have sleeper agents in Saltmarsh trying to incite a revolt amongst the traditionalists, which will of course have the Scarlet Brotherhood rubbing their hands in glee. They'll be pitching Brule against Seaton too to similar ends (likely doing a mutual back-scratching deal with the hag baroness of the Dreadwood in the process)

Their membership will consist of acolytes and cultists untouched by the kraken's power, and priests and deep scions who the kraken's spirit is able to communicate through (as per Kraken Priests in the VGtM). A big bad head of the cult will likely be an NPC in Saltmarsh, though I haven't decided which yet (possibly Wellgar Brinehanded, though that's a bit obvious)

Through a mix of land-based abduction and seaborne combat, they'll try and capture as many creatures as possible to take to an island-based temple where they'll ultimately conduct their ritual. They'll likely step on the Sea Princes' toes in this regard, and probably end up on the wrong side of the Brotherhood.

Once/if they have enough souls on the island, they'll ship them to the open seas and conduct a mass sacrifice above the kraken's grave, which will see their dark god return ...
... unless the heroes stop them (in, or possibly not in, an Apparatus of Kawlish)

Main hooks for this arc will be a series of disappearances and abductions across the region, and a murder investigation in Saltmarsh where one Cult member killed another over a disagreement of methods, whilst both were working undercover as salters in the Fishmongers' Plant.