Yes

Student or Learner
"The interview ended abruptly, leading to speculation it had been cut short."
Is there a "that", which might be there after speculation, omitted?
Yes
"That" probably should not have been omitted in the above.
I would use 'that', but the version without seems OK to me.
The sentence doesn't make any sense. If it ended abruptly, then it was cut short. No need to speculate.
I think meetings can end abruptly without necessarily being cut short.