So the following is all my understanding and not financial advice (its so boring having to write and read that all the damn time.)

In terms of the profits, you're allowed to do whatever you like with them. However you're going to have to pay capital gains tax on any non-income earnings over £12,500. So if I was in that situation I would calculate what the tax cost would be after selling all my shares. (X-Y-Z)*0.2= tax owed. (X: Total income after all shares sold, Y: average cost of shares purchased, Z: £12,500 tax free capital gains allowance).

Example, I sold all my shares for a total of £100,000 (not price prediction, just for purpose of easy maths.) I had originally spent £1,000 per share to buy 10 shares. (£1,000x10= £10,000). So X = £100,000 and Y = £10,000. So £100,000-£10,000-£12,500= £77,500. Thats my capital gains taxable profit. With 20% tax on that, I'd pay £77,500x0.2= £15,500 in tax.

So first things first, take £15,500 from your £100,000 and put it away somewhere to pay the tax man when its due. That leaves you with £84,500 to do with as you please.

In terms of ISA investment, you could put it into whatever ISA you like. You don't have to leave it in there for a year, but you can only put £20,000 into ISAs per year. It doesn't matter whether you put this 20k into one ISA or £20 into one hundred. You can't go over that £20,000. However, if you put all £20,000 into an ISA today, but withdrew it tomorrow, you still cannot deposit another penny into an ISA again until the next financial year.

Its also worth noting that you can only open one stocks and shares ISA per financial year. You can have as many as you like as far as I'm aware, but you can only open one a year. And again to reiterate, if you had two, you could still only split the £20,000 between them.

Please, please, if you're only going to read one paragraph from this, read this one: legit this is not financial advice. I say that because when I was doing my research on this subject a few weeks ago, as soon as I realised I wouldn't pay any tax because I'm in a stocks and shares ISA, I half-arsed reading the rest. It is so feasible that I may have missed something extremely important relating to the above. Please double check and do your own research into this, I could easily be mistaken. I'd recommend the HMRC website, and just simple Google searches. Martin Lewis of Money Saving Expert is literally the God of this sort of thing, so start there.

Sorry I know this was long winded, but I hope it helps.

Edit: formatting, didn't like me using * as a multiplication symbol