From 3's Website

Your account must be up to date (it must not be in arrears)

    You must have a contract with us, and you must have been with us for a
minimum of three months. If you're on ThreePay, you do not qualify for
an upgrade. If you've completed 11 months of your contract, you'll be
eligible for a number of upgrade offers, including free ones. If you
haven't completed 11 months of your contract, you still qualify for an
upgrade, but you have to pay for it.

If you qualify
To get a handset upgrade, here’s what you need to do.

    Contact one of our specialist upgrade advisers.
Phone 333 and select option 1 and then option 5 and then option 1.
Or    
    Visit one of our 3Stores or 3Points in Superdrug. You’ll need to prove
your identity and address.
To prove your identity, you need to have one of these things with you:
credit or debit card, full driving license, photo card provisional
driving license or passport.
To prove your address, you need to have one of these: utility or council
tax bill, full driving license, photo card provisional driving license,
band or building society or credit card statement, family allowance or
pension book. You can also visit one of our many high street retailers.