1.
If you carry on doing something, you continue to do it.
The assistant carried on talking...
Her bravery has given him the will to carry on with his life and his work...
His eldest son Joseph carried on his father's traditions...
'Do you mind if I just start with the few formal questions please?'-'Carry on.'
= continue
PHRASAL VERB: V P -ing, V P with n, V P n (not pron), V P
2.
If you carry on an activity, you do it or take part in it for a period of time.
The consulate will carry on a political dialogue with Indonesia...
= conduct
PHRASAL VERB: V P n (not pron)
3.
If you say that someone is carrying on, you are irritated with them because they are talking very excitedly and saying a lot of unnecessary things. (INFORMAL)
She was yelling and screaming and carrying on...
He was carrying on about some stupid television series.
= make a fuss
PHRASAL VERB: V P, V P about n [disapproval]