The phrase "calming influence" means that someone or something has a soothing effect and helps to make a situation or atmosphere more peaceful and relaxed. Full definition
First ladies are also seen as calming influences on presidents. (fortune.com)
At least 2 more experienced players who can act as calming influences late in late matches. (sophieenglandofficial.com)
You've been a wonderfully calming influence and have taught me a great deal about what is required in a situation like this and how to approach things. (brownejacobson.com)