Since 2014, Gillespie has been vegan. "It was probably a year or so after my dad passed away, and I think naturally you just want to look after yourself.
"It started off as a health thing, and I'm very conscious of how we treat non-humans on our planet, and it's something I'm pretty passionate about.
"The more research that one does, the simpler and clearer it is. We don't treat animals very well — that's just a fact. For a start, we eat them. And we just don't treat them with any form of respect whatsoever.
"I find that ethically wrong. From a health point of view, it's bad for you, and for our environment it's just not sustainable."
Gillespie frequently uses his Twitter account to draw attention to these issues. "Being a vegan and animal advocate, if someone asks me a question and wants to learn about it, then I'm happy to pass that on and have the discussion. I don't get angry with people. Everyone's different.
"I think as a general rule people know that we don't treat animals particularly well ... and being a vegan is growing at a rapid rate.
"The penny's dropping — it just might take longer for some people but that's fine".
If such concerns seem a little out of kilter with cut-throat professional sport, this has not been Gillespie's experience. "I've actually found it to be very open and accepting," he reflects. "People go out of their way to help — like you go to county grounds, and there's an option there for you to eat, and just small things like that. So I see progress. It's a good sign."
Ultimately, Gillespie hopes that the cricket ball itself can be made from an alternative to leather.
These days, whenever the Australia or England cricket coaching jobs are discussed, Gillespie's name is mentioned. Strangely, though, he does not consider the coach as important in cricket as, say, football. "Our job is to observe, and watch the game, ask good questions, and listen. I think listening is a very important skill to have as a coach," he reflects.
"It's telling players be true to yourself — play your game, trust that knowledge of all the hard work you've put in — and then just go and play. You will entertain people. If you go out there with pride and passion, and people see that you are doing something you love and you've got a smile on your face, that's going to rub off on people".
Gillespie views himself as an enabler for players to think critically about their own games and learn from each other. "That's what I really want — lads in cricket conversation about the game, sitting talking about what is going on out there. And for me, the more cricket conversations you can have, the more you learn."
For all his deep thinking about the sport, Gillespie aims to simplify the game for his players. Where once he would plan training sessions meticulously, he now has more unstructured sessions.
"We want adaptable players. We don't want adapted players. If players are just being told what to do all the time, that puts them off thinking for themselves as much as they should. On the cricket field, they've got to work it out for themselves", he says.
"We're not making any predictions, and we're not focusing on results, we're focusing on what we're actually doing in the games: can we just keep chipping away and be better each time? And most importantly, the big thing is what do we learn from in every training session, what can we learn from each and every day's play throughout the season?"
- Telegraph Group Ltd