We had a member of staff that set up his own business outside of our work, but doing the same type of work.
We didn't know about it and only found out accidentally as he left something on our office server and someone found it. A little bit more digging and we found his business online and discovered that he was advertising as being open Monday to Friday, 9am to 5.30pm. i.e. exactly the same hours he was supposed to be working for us!
This was all post-Covid and while we had been a bit concerned about his progress on work for a while, we were also aware that he was having to work from home in a 1 bed flat with his wife and two toddlers, so (foolishly) gave him the benefit of the doubt during difficult times.
Once we realised what was going on, we dealt with it on a performance management basis, by discussing the poor turnaround of work and asking him to come back in to the office full time. He wasn't very happy about it, for obvious, but unspoken reasons. This combined with a bit of extra pressure to turn around jobs in a better timeframe forced his hand, without us having to go down the disciplinary route.
Within a month of being back in the office, he'd put his notice in, telling us he'd got another job with another firm. I'm not sure if he ever actually started working for them, or whether he then just went to work for himself full time.
We were ready to go down the disciplinary route if it had carried on, especially as we had a no-compete clause in our contract (or rather, he needed to inform us if he did other work as confidentiality and conflict of interest is important in our industry).
@dodgylady23 - if your pisstaker is an actual employee, I'd speak with HR as this is clearly a disciplinary matter. You'd have to go through an investigation process and hold an investigation meeting with her to establish her side of the story formally, then take it from there. Try not to give too much away to her at the moment in terms of your investigation.
ACAS has some useful information - ACAS, but hopefully you have an internal (or external) HR department that can deal with a lot of it for you.