Usage patterns
〈事〉に余裕があるto have some leeway (in time, money, etc.)
This month we have some room in the budget.
余裕の表情a composed, unruffled expression
He faced the exam with a calm, composed expression.
〈人〉に余裕がないto have no time/room to spare
I've been so busy lately that I have no room to breathe.
心に余裕があるto have inner calm/room to spare mentally
Thanks to the trip, I gained some mental composure.
余裕を持つto keep some margin/composure (in doing something)
It's better to prepare with some margin to spare.
Expressions
余裕をかますfeign composure; act like one has something to spare 余裕を与えるgive someone space; give breathing room; cut some slack