"continue the adventure" is correct and usable in written English.
You can use it when you want to encourage someone to pursue a certain activity or journey. For example, you could say "Gather your courage and continue the adventure!".
BioShock 2 hopes to continue the adventure.
I want to continue the adventure but not with [just] anyone.
The initial program, on October 12th, featured Bartók's First and Fifth Quartets, as well as a fascinating work by a brilliant contemporary Hungarian, Peter Eötvös; the final two concerts continue the adventure.
In the weeks ahead, thousands of young cadets will begin or continue the adventure of a lifetime as an unprecedented gathering of tall ships set a course for East Coast ports from Miami to Portland, Me.
At some point they will have to put the venture on a more formal footing – with trustees and the possibility that one of their children might want to continue the adventure in future.
We will be able to continue the adventure at a bigger scale".
The photographs continue the adventures of the fictional British Excavation Corps, this time as they encounter a tribe of Nordic bog-dwellers whose caps, loincloths and unusual garments seem straight out of Bosch.
Mr. Colfer will continue the adventures of Arthur Dent through the cosmos in the new book, to be titled "And Another Thing... .. Around 16 million copies of the books have been sold around the world and translated into 35 languages.
Mr. Reubens, who is preparing his live Pee-wee Herman Showw" for Broadway, has spoken often about two Pee-wee-centered film scripts he has written that would continue the adventures of his manic character, seen in "Pee-wee's Big Adventure" and the CBS children's series "Pee-wee's Playhouse".
Set three years after the events of Outlaw Star, it was to continue the adventures of Gene Starwind and Jim Hawking in their new starship named "Sword of Wind".
