to do something that shows that you have power
Senior figures in the party have urged Dr Garner to assert his authority ahead of Sunday's elections.
to present and demand recognition of (a legal right)
The McNeils asserted a claim against the manufacturer when, as a result of a design fault, their car burst into flames.
to state something confidently
He went on to assert that overdraft terms could still be assessed for their fairness for reasons other than price. For instance, if customers were taken by surprise.