Advice on my garden please

[Surpriseeggsforbreakfast]

I’d like to create a new border on the right side of the garden and also get rid of the raised beds on the left side (in second picture). Would this be expensive to have done professionally? could my gardener dig out the border for me?

A competent gardener should know how to create a border. If it's quite a big border, however, they might well want a turf- stripper to do it ie if they're a one-person business, they might ask you to cover hire-cost, perhaps.

Removing the raised beds - not sure, to be honest, but if you're happy with their work, I'd certainly give them first refusal. Have a chat and ask for a quote.

Tbh, if that was my garden I would do the border myself, it's not difficult, just hard work. The turf can be removed with a spade and if you pile it up upside down (out of the way somewhere)the grass will die off, it will just become a pile of soil and you can re-use it. Dig over the new bed, buy in some bagged topsoil to top dress and feed it and then have fun designing a planting plan. You can mark the edge of your new bed with string or spray paint before you start
I think your raised beds look rather good actually. I'm quite envious. Can you not tidy up and treat the wood, add top soil if necessary and plant? They would be brilliant for veg.
I quite understand, though, if you are not into hard labour and prefer to get someone in, but the money you save could be spent on some wonderful plants instead.

Are the raised beds acting as terracing? The garden next door looks higher than yours, judging by the fence.