Usage patterns
〈事〉に支障が出るfor a problem/hindrance to arise affecting something
The construction noise is causing problems for the neighborhood's daily life.
〈事〉に支障をもたらすto cause a hindrance to something
The typhoon caused disruptions to transportation.
支障はないthere is no problem/it won't cause any trouble
I don't think this change will cause any problems for the work.
〈事〉の支障になるto become a hindrance to something
Noise becomes a hindrance to work.
Expressions
支障をきたすhinder; obstruct; interfere with; cause a problem