I have done this over the last 12 months. I am in my late 50s too.
First, I worked on losing weight, and during that phase I retired clothes that got too big but didn't buy new ones or change my style. I was still working, mainly from home and managed to get through the phase without needing to buy clothes in an interim size. I also dragged some clothes in smaller sizes from the depths of my wardrobe; they weren't fashionable, but they did.
Then, when I reached a weight that was going to stick and decided to quit my job, I was ready to start choosing a style that would suit my new lifestyle.
The office-style trousers, blouses and smart shoes are gone, as are the black and corporate colours. I now have a soft, muted wardrobe of blues, teals and pinks which really suit me and my life. The only thing left from my previous wardrobe is my funeral outfit, which could double up if I ever needed a formal meeting outfit.
I found the brands that I liked, then used Vinted and eBay to buy at reasonable prices, mainly new with tags at at least 50% below retail. I have more than a capsule wardrobe, but it is all mix-and-match.
I am still selling my old wardrobe via Vinted, it is a slow process, but will help to pay for my new items.