MySQL on insert in table update field in another table?
Something like this should do the trick.

DELIMITER $$
CREATE TRIGGER My_Trigger -- name is arbitrary
AFTER INSERT ON TopicAnswers
FOR EACH ROW
BEGIN
  UPDATE Topics
    SET Answers = Answers + 1
    WHERE ID = NEW.TopicID;  -- The OP figured this line out for himself.
END;
$$
DELIMITER ;


I don't have your data, but it should get you started.

Take the trouble to go to the Help Centre, take the tour
and check out the "help us to help you" blog. This forum
is a great resource and you will get all the more out of
it if you take the trouble to read the guidelines (not that
there's anything wrong with your post). p.s. welcome to the
forum.