No, you'll still be able to save up to the personal allowance in each new tax year. The four-year fixed-rate applies to the interest you will earn on the money you deposited in that particular tax year.
If you plan to open the four-year Isa now, you need to be careful because the Isa rules will be changing in July.
The current limit for the 2014/15 tax year is £11,880, of which £5,940 can be invested into a cash Isa. In each tax year, you're only able to invest into one stocks and shares Isa and one cash Isa.
If you invest now, in July your current Isa will automatically become a New Isa with an annual allowance of £15,000 and you can then, in theory, top up your stocks and shares or cash Isa to the new limit.
However, your provider may not accept new money into your 2014/15 Isa, perhaps because the four-year fixed deal is closed. You should therefore check to see if it will accept additional investments after 1 July. If it won't, you might need to reconsider whether to invest in the first place.