I thought perhaps as a start we should define what is meant by rapport, as I remember not having really heard this word prior to my first coach training.
"harmonious accord or relation that fosters cooperation, communication, or trust"
(of course other definitions are available! This one was just one of the shorter ones)
Cooperation, communication, and trust eh?! Probably useful for our client relationships then? At the very least I can promise you that if this is in place it will make your life easier.
And as much as my ah-ha moment occured when someone put a word to something that I appeared to do naturally, had not thought it was a skill or gave any credit to, once it came into my awareness it explained why I have always found it easy to get on with people (and haven't been smacked by a client yet - not a coaching client that is ha but a criminal one. And yes I wish I was joking but it does happen).
So why is rapport a thing? Why is it important to even care about? Well, evolutionary-wise we like people who are like us, think like us, move like us, speak like us, etc. Same-ness makes us feel safe. It increases our feeling of being understood and not judged.
Whilst you can probably recall a person that you just seem to rub up wrongly against or feel like you instinctively would rather just avoid, and you can likely name the things that destroy or damage rapport (interrupting for example), do you know how one can build it? On purpose. To start consciously doing a few things that you actually find easy, including maybe just checking in with how it is going, and then assessing whether you need to tweak your approach to just bump it up a bit?
Some of it goes into that initial snap decision we make unconsciously when we first meet someone. Which for us, means don't lose rapport before we have had a chance to make it!
So in the professional world, that can mean just considering whether you look the part of what they are likely expecting from their expert. Is the background on your camera appropriate? If not, use blur or a virtual background. Also with virtual meetings, please please please consider the camera angle! You are meant to be centre screen and face on. So if you have a second screen with information on that you will be using in the meeting then say as much. Explain why your eyes may shift to the right or left - so they don't think you are bored, watching tv, or looking out of a window.
Then whilst in the meeting (virtual or not), just spare a moment to consider how they speak. Are they fast or slow, loud or quiet? Can you match this? What about body language? Are their arms all over the place whilst they talk? Can you free your arms and hands up a touch when you next talk? And note what I said there - 'free them up' - 'a touch'. You do not want to freak them out. Moving your hand back and forth can be sufficient if you are not a natural arm mover. And if it just isn't in your comfort zone then just don't do it. You will come across odd and fake.
Have they their legs or arms crossed? Are they leaning forward or back and can you subtley do the same? Again, we don't need extravagent gestures here - these are subconscious signals - both in their execution and in their being picked up on - so most people aren't even aware of them. In fact you do not want them to be overtly aware of what you are doing, as it can then be intrepreted as manipulative or like you are taking the piss out of them.
Also you don't need to think about it consistently. Just notice when things feel a little less than easy with them and see if you can just match one thing - it could be slowing down your speech just a touch. And then forget about it. Get back to focusing on your client and their life.
I should also say, the only time I would tell you not to match a client is if they are shouting (or telling you to fuck off :0) - see previous story). If they are loud, shouting, and appear angry, then we do the opposite (that is, if you feel safe enough to stay in their vicinity). We keep our voice just a tiny bit under normal speaking volume, and we stay nice and calm and relaxed, whilst being clearly engaged in understanding what they are frustrated or unclear about. Anger is a protective response to feeling fear. For example, fear of being disrespected, fear of losing something we care deeply about, fear of others thinking less of us, etc. Shouting is typically a by-product of the surge of energy that comes with anger and fear - fight or flight response. Which is why it's usually really obvious when they run out of steam.
