This construction evidently means that a particular result is being expressed by the ἵνα clause or ἵνα + subjunctive. It is conveying an idea regarding the new commandment's content (see Rogers and Rogers Linguistic and Exegetical Key to the Greek NT, page 216).
For the use of ἵνα as a result conjunction, see Daniel B. Wallace, Greek Grammar Beyond the Basics, p. 677. Compare John 9:2.
Think of the ἵνα + subjunctive clause as being translated "with the result that . . ."
NET Bible Footnote: tn The ἵνα (hina) clause gives the content of the commandment. This is indicated by a dash in the translation.
"I am giving you a new commandment, that you love one another; just as I have loved you, you also love one another" (John 13:34 Revised NWT).
"I give you a new commandment, that you are to love each other: that as I loved you, you too are to love each other" (Byington).
Some understand the construction to be a purpose clause instead of communicating the result. From Vincent's Word Studies
With its usual telic force; indicating the scope and not merely the form or nature of the commandment.
See also http://place.asburyseminary.edu/cgi/viewcontent.cgi?article=2323&context=asburyjournal