Here is the item again:
Derek wanted a ferocious pit bull terrier to scare off burglars, but his
apartment complex did not allow dogs as a result,
Derek had to settle for naming his goldfish Mr. Jaws and installing additional
door locks.
His apartment complex did not allow dogs is a main clause. As a result, Derek had to settle for naming his goldfish Mr. Jaws ... is a second main clause. Because these two clauses run right into each other with no break, they create a fused sentence.
A semicolon would go nicely in the empty space between dogs and as.