Your dec ision is actually rather more complex than it first appears. The problem is that the limits on what you can pay into the HTB ISA might make it less attractive - it will all depend.
Currently, you can put £15k/year into a normal ISA (Either Cash, or Stocks and Share or a combination). The HTB ISA only allows £200/month = £2,400/year. Since you can only pay into one Cash ISA in any one year you are going to lose out on the other £12,600 that you could save and grow tax free. Having said that, the 25% contribution by the govt. is extremely attractive and probably outweighs any tax saving.
It is not so clear whether you can contribute to a HTB ISA (cash) and put the rest of your allowance into a Stocks and Shares ISA - if you can, you should seriously consider doing so. Yes this exposes you to a riskier investment (shares can go down as well as up etc.) but the benefits can be significant (and the gains are tax free).
As said above, the rules are that money you have paid into an ISA in earlier years is separate - you can't pay any more into the "old" one whilst paying into a "new" one but you don't have to do anything with the "old" ISA.
But you might WANT to do something since institutions are amazingly mean (underhand) in their treatment of customers. You may well find that the interest rate you get on your "old" ISA becomes less competitive over time. You should (Must) check every year what rate you are getting and whether you can get a better rate in a different ISA - if there is a better rate ISA and if it allows transfers IN, you should arrange to make the trasnfer - you ABSOLUTELY MUST TRANSFER between ISAs - never even think of taking the money out and then trying to pay it in to another ISA, it must be transferred directly between ISAs.
So overall, yes, stop paying into the "old" ISA, open a new HTB ISA next year and if you can pay in the maximum do so. But if you can afford to save more, you might be able to open a Stocks and Shares ISA as well and pay into that too (max £15k into the pair in one year). And then do not "forget" about the "old" ISA(s) you will probably need to move all the money you have in the "old" one(s) regualrly into new ISAs to obtain a sensible rate.
You might do well to read up on all this a lot more - I strongly recommend the site http://www.moneysavingexpert.com/ which gives a lot of helpful advice about everything to do with money (no I don't have any association with them).
