Hi,
which sentence is correct: They are both fine. It's a matter of style.
"I am sorry for the delay in replying, and hope ...."
"I am sorry for the delay in replying, and I hope...."
When can I omit the subject pronoun from the second sentence? Very generally speaking, when the sentence is sufficiently short and simple that the reader has not 'forgotten' the subject by the time he reads the second verb.
{Don't think of this as two sentences. It's two clauses in one sentence. }
Best wishes, Clive