After a long break in our conversation, we began to speak again.
ーWe started talking again after a long silence.
「長い沈黙の後、私たちはまた話し始めた。」
started talking again で「また話し始めた」
started to talk again でも大丈夫です。
「長い沈黙の後」は after a long silence と言えます。
ーAfter a long break in our conversation, we began to speak again.
「会話中長い中断の後、私たちはまた話し始めた。」
after a long break で「長い中断の後」
began to speak again で「また話し始めた」
ご参考まで!