I believe that would be a judge's discretionary item or something you would have to request. (Someone will correct me if I am wrong.) I believe that it would have to be specified in the Order. My ex was litigation-happy and took me to court 6 times after he was ordered to pay costs and despite strong protestations from my lawyer (Alberta Court of Queens Bench).
In Ontario:
Prohibition on Further Motions
(3) On making an order under subrule (1), the court may also make an order under rule 37.16 prohibiting the moving party from making further motions in a proceeding without leave. O. Reg. 43/14, s. 1. (Rules of Civil Procedure)
and
Contested Motion
57.03 (1) On the hearing of a contested motion, unless the court is satisfied that a different order would be more just, the court shall,
(a) fix the costs of the motion and order them to be paid within 30 days; or
(b) in an exceptional case, refer the costs of the motion for assessment under Rule 58 and order them to be paid within 30 days after assessment. O. Reg. 284/01, s. 16.
(2) Where a party fails to pay the costs of a motion as required under subrule (1), the court may dismiss or stay the party’s proceeding, strike out the party’s defence or make such other order as is just. R.R.O. 1990, Reg. 194, r. 57.03 (2) (Rules of Civil Procedure).